user315: How does the new quintuple-repetition rule work, please?
To be clear: my question does not concern how likely the rule and its cases are to arise in practical play, but rather just what the rule is, in cases in which it might theoretically apply.  Technically precise answers which (i) illuminate possible misunderstandings and (ii) consider edge cases merit extra appreciation.
Also, if you happen to know:  Have authors, masters and/or tournament directors concurred (to the extent to which they care) in the meaning of the new quintuple-repetition rule?  Or does the rule as written admit technical ambiguity?
References:

FIDE.  Laws of Chess, July 2014.  Refer especially to sect. 9.6.
Geurt Gijssen.  Arbiter's Notebook.

UPDATE: EXAMPLE
In light of @dfan's comment, an example:
[Title "White to move, illustrating sect. 9.6"]
[FEN "2b2rk1/5ppp/8/8/8/8/5PPP/2B2RK1 w - - 0 1"]

1. Bb2 Bb7 2. Bc1 Bc8 3. Ba3 Ba6 4. Bc1 Bc8 5. Bd2 Bd7 6. Bc1 Bc8 7. Be3 Be6 8. Bc1 Bc8

Drawn?  Why or why not?

user24210: The only question is whether the same position has occured ( = the FEN notation would be the same) multiple times ( = five different # of moves apply to the same position). Nothing is said about move sequences.

user5860: During the FIDE refresher course for International Arbiters, it has been strongly recommended to apply this rule very strictly. Which means that IA are strongly encouraged to change an already signed result if it is later discovered that a quintuple repetition has occurred. 
After a quintuple repetition, the game is drawn without any formality, no claim is required. The game is also implicitly over, meaning that all that happens after is irrelevant. For the 75 moves draw, if there is a mate, it will prevail. 
If the result reported by the players is anything other then a draw, this means that both players have, wilfully or not, signed a wrong result. This situation is governed by Article 8.7   
At the conclusion of the game both players shall sign both scoresheets, indicating the result of the game. Even if incorrect, this result shall stand, unless the arbiter decides otherwise.  

user8201: In the Jan 2018 Laws (and indeed the previous version too, but that's history) the rule is replaced with:

9.6.1 [The game is drawn if] the same position has appeared, as in 9.2.2 [Draw by Repetition] at least five times.

And the game ends immediately, like mate, pat, dead position & 75 moves. So this issue is resolved. I do feel that, little by little, the FIDE Laws are improving.

user315: The commenters seem to agree unanimously—and please pardon the necessary formalism!—as follows:  Quintuple repetition arises when, and only when, the position on the chessboard is the same after moves n, n+2, n+4, n+6 and n+8 for any nonnegative n, where n need not be an integer but 2n is indeed an integer.
For example, quintuple repetition arises if the position is the same after 31.5, 33.5, 35.5, 37.5 and 39.5 moves—that is, if the position is the same after White's 32nd, 34th, 36th, 38th and 40th moves.  Whether positions after 38, 38.5 and/or 39 moves happen also to repeat earlier positions is irrelevant to the rule.
The example given in the question is indeed a draw by quintuple repetition.

user4418: First note that your link to Geurt Gijssen. Arbiter's Notebook. is broken. ChessCafe.com have put almost all their stuff behind a paywall.
The purpose of this rule and of the related 75-move rule (after 75 moves with no captures or pawn moves the arbiter can / must step in and declare a draw) are for the benefit of arbiters. In summary they are the "I've got a home to go to and a warm bed waiting for me" rules. The key point here being that these two rules do not require a player to make a claim but instead the arbiter can intervene to stop the game.
Your example is not a draw under the rule. Here is how it works:
White's alternate moves must be identical.
Black's alternate moves must be identical.
For 5 consecutive, alternate White's turns the position must be identical.
For 5 consecutive, alternate Black's turns the position must be identical.
If that gobbledygook sounds confusing here is an example of a drawn game under the new rule:
1) Nc3 Nc6
2) Nb1 Nb8
3) Nc3 Nc6
4) Nb1 Nb8
5) Nc3 Nc6
6) Nb1 Nb8
7) Nc3 Nc6
8) Nb1 Nb8
9) Nc3 Nc6
10) Nb1 Nb8
11) Nc3 Nc6
Note that after Black's 4th move White could have claimed a draw under the 3-fold repetition rule and after White's 5th move either player could claim a draw on their turn. 
If either player deviates from the strict repetition then the conditions are not fulfilled. For instance if White's 3rd and 4th moves are Nf3 and Ng1 then the strict sequence required for the satisfaction of the rule is broken.
Note that the rule says "for at least five consecutive alternate moves by each player". If it said "either player" instead of "each player" then the position and sequence in question would be a draw. But the example fails because it is only identical before alternate White moves and not before alternate Black moves.
Since 3-fold repetition draws can only be claimed when the moves are recorded they cannot normally be claimed during rapid and blitz games. The new rules allow the arbiter to intervene and stop the game provided he has witnessed and noted the moves and continue with the next round or go home to bed.
30/12/2014: There were two International Arbiters at our club annual rapid championship last night. I asked one of them and he was very clear. The rule:

the same position has appeared, as in 9.2b, for at least five
  consecutive alternate moves by each player.

according to him means that after 5 alternate white moves the position must be the same in the meaning of 9.2b and after 5 alternate black moves it must be the same in the meaning of 9.2b and that this sequence of moves must be consecutive i.e. the first repeating black position must come immediately before or immediately after the first repeating white position and not part way through the sequence.
PS It's probably worth noting the answer he gave to a supplementary question.
Question: What happens if after one player wins through resignation / checkmate / flag fall it is discovered that there was an earlier 5 fold repetition? Should the result be changed to a draw?
Answer: Emphatically no. Just as the 3 fold repetition rule is for the benefit of the players, they may choose to claim by it or not at the specific time the incident occurs, so is the 5 fold repetition rule for the benefit of the arbiter, he may choose to enforce it or not at the time the incident occurs. He may not enforce it retrospectively. The win stands.
Edit: Well, it seems that the IA I consulted was wrong. Hidden away in section 6.2a of the FIDE Handbook it says this

A move is also completed if: 1.the move ends the game (see Articles
  5.1.a, 5.2.a, 5.2.b, 5.2.c, 9.6a, 9.6b and 9.7)

9.6a and 9.6b are the two new draw rules, 5-fold repetition and 75 moves with no captures or pawn moves. So, they are elevated by this throw-away clause to the same level as checkmate, stalemate, resigns and agreed drawn. The arbiter has no more choice than he does with checkmate, etc.

315: <p>How does the new quintuple-repetition rule work, please?</p>

<p>To be clear: my question does not concern how likely the rule and its cases are to arise in practical play, but rather just what the rule is, in cases in which it might theoretically apply.  Technically precise answers which (i) illuminate possible misunderstandings and (ii) consider edge cases merit extra appreciation.</p>

<p>Also, if you happen to know:  Have authors, masters and/or tournament directors concurred (to the extent to which they care) in the meaning of the new quintuple-repetition rule?  Or does the rule as written admit technical ambiguity?</p>

<p>References:</p>

<ul>
<li><a href="http://www.fide.com/component/handbook/?id=171&amp;view=article" rel="noreferrer">FIDE.  <em>Laws of Chess,</em> July 2014.</a>  Refer especially to sect. 9.6.</li>
<li><a href="http://www.chesscafe.com/archives/archives.htm#An%20Arbiter%27s%20Notebook" rel="noreferrer">Geurt Gijssen.  Arbiter's Notebook.</a></li>
</ul>

<p><strong>UPDATE: EXAMPLE</strong></p>

<p>In light of @dfan's comment, an example:</p>

<pre><code>[Title "White to move, illustrating sect. 9.6"]
[FEN "2b2rk1/5ppp/8/8/8/8/5PPP/2B2RK1 w - - 0 1"]

1. Bb2 Bb7 2. Bc1 Bc8 3. Ba3 Ba6 4. Bc1 Bc8 5. Bd2 Bd7 6. Bc1 Bc8 7. Be3 Be6 8. Bc1 Bc8
</code></pre>

<p>Drawn?  Why or why not?</p>
 24210: <p>The only question is whether the same position has occured ( = the FEN notation would be the same) multiple times ( = five different # of moves apply to the same position). Nothing is said about move sequences.</p>
 5860: <p>During the FIDE refresher course for International Arbiters, it has been strongly recommended to apply this rule very strictly. Which means that IA are strongly encouraged to change an already signed result if it is later discovered that a quintuple repetition has occurred. </p>

<p>After a quintuple repetition, the game is drawn without any formality, no claim is required. The game is also implicitly over, meaning that all that happens after is irrelevant. For the 75 moves draw, if there is a mate, it will prevail. </p>

<p>If the result reported by the players is anything other then a draw, this means that both players have, wilfully or not, signed a wrong result. This situation is governed by Article 8.7   </p>

<p>At the conclusion of the game both players shall sign both scoresheets, indicating the result of the game. Even if incorrect, this result shall stand, unless the arbiter decides otherwise.  </p>
 8201: <p>In the Jan 2018 Laws (and indeed the previous version too, but that's history) the rule is replaced with:</p>

<blockquote>
  <p>9.6.1 [The game is drawn if] the same position has appeared, as in 9.2.2 [Draw by Repetition] at least five times.</p>
</blockquote>

<p>And the game ends immediately, like mate, pat, dead position &amp; 75 moves. So this issue is resolved. I do feel that, little by little, the FIDE Laws are improving.</p>
 315: <p>The commenters seem to agree unanimously&mdash;and please pardon the necessary formalism!&mdash;as follows:  Quintuple repetition arises when, and only when, the position on the chessboard is the same after moves <em>n,</em> <em>n+2,</em> <em>n+4,</em> <em>n+6</em> and <em>n+8</em> for any nonnegative <em>n,</em> where <em>n</em> need not be an integer but <em>2n</em> is indeed an integer.</p>

<p>For example, quintuple repetition arises if the position is the same after 31.5, 33.5, 35.5, 37.5 and 39.5 moves&mdash;that is, if the position is the same after White's 32nd, 34th, 36th, 38th and 40th moves.  Whether positions after 38, 38.5 and/or 39 moves happen also to repeat earlier positions is irrelevant to the rule.</p>

<p>The example given in the question is indeed a draw by quintuple repetition.</p>
 4418: <p>First note that your link to Geurt Gijssen. Arbiter's Notebook. is broken. ChessCafe.com have put almost all their stuff behind a paywall.</p>

<p>The purpose of this rule and of the related 75-move rule (after 75 moves with no captures or pawn moves the arbiter can / must step in and declare a draw) are for the benefit of arbiters. In summary they are the "I've got a home to go to and a warm bed waiting for me" rules. The key point here being that these two rules do not require a player to make a claim but instead the arbiter can intervene to stop the game.</p>

<p>Your example is not a draw under the rule. Here is how it works:</p>

<p>White's alternate moves must be identical.
Black's alternate moves must be identical.
For 5 consecutive, alternate White's turns the position must be identical.
For 5 consecutive, alternate Black's turns the position must be identical.</p>

<p>If that gobbledygook sounds confusing here is an example of a drawn game under the new rule:</p>

<p>1) Nc3 Nc6
2) Nb1 Nb8
3) Nc3 Nc6
4) Nb1 Nb8
5) Nc3 Nc6
6) Nb1 Nb8
7) Nc3 Nc6
8) Nb1 Nb8
9) Nc3 Nc6
10) Nb1 Nb8
11) Nc3 Nc6</p>

<p>Note that after Black's 4th move White could have claimed a draw under the 3-fold repetition rule and after White's 5th move either player could claim a draw on their turn. </p>

<p>If either player deviates from the strict repetition then the conditions are not fulfilled. For instance if White's 3rd and 4th moves are Nf3 and Ng1 then the strict sequence required for the satisfaction of the rule is broken.</p>

<p>Note that the rule says "for at least five consecutive alternate moves by <strong>each</strong> player". If it said "either player" instead of "each player" then the position and sequence in question would be a draw. But the example fails because it is only identical before alternate White moves and not before alternate Black moves.</p>

<p>Since 3-fold repetition draws can only be claimed when the moves are recorded they cannot normally be claimed during rapid and blitz games. The new rules allow the arbiter to intervene and stop the game provided he has witnessed and noted the moves and continue with the next round or go home to bed.</p>

<p>30/12/2014: There were two International Arbiters at our club annual rapid championship last night. I asked one of them and he was very clear. The rule:</p>

<blockquote>
  <p>the same position has appeared, as in 9.2b, for at least five
  consecutive alternate moves by each player.</p>
</blockquote>

<p>according to him means that after 5 alternate white moves the position must be the same in the meaning of 9.2b and after 5 alternate black moves it must be the same in the meaning of 9.2b and that this sequence of moves must be consecutive i.e. the first repeating black position must come immediately before or immediately after the first repeating white position and not part way through the sequence.</p>

<p>PS It's probably worth noting the answer he gave to a supplementary question.</p>

<p>Question: What happens if after one player wins through resignation / checkmate / flag fall it is discovered that there was an earlier 5 fold repetition? Should the result be changed to a draw?</p>

<p>Answer: Emphatically no. Just as the 3 fold repetition rule is for the benefit of the players, they may choose to claim by it or not at the specific time the incident occurs, so is the 5 fold repetition rule for the benefit of the arbiter, he may choose to enforce it or not at the time the incident occurs. He may not enforce it retrospectively. The win stands.</p>

<p>Edit: Well, it seems that the IA I consulted was wrong. Hidden away in section 6.2a of the FIDE Handbook it says this</p>

<blockquote>
  <p>A move is also completed if: 1.the move ends the game (see Articles
  5.1.a, 5.2.a, 5.2.b, 5.2.c, 9.6a, 9.6b and 9.7)</p>
</blockquote>

<p>9.6a and 9.6b are the two new draw rules, 5-fold repetition and 75 moves with no captures or pawn moves. So, they are elevated by this throw-away clause to the same level as checkmate, stalemate, resigns and agreed drawn. The arbiter has no more choice than he does with checkmate, etc.</p>
