<s>[INST] Write $π = (3, 2, 5)(2, 5, 4)$ in “table” notation? Isn't this impossible...? Because this permutation goes from 3 --> 2 ---> 5 ---> 3 according to the first cycle, but goes from 2 --> 5 ---> 4 ---> 2 according to the second cycle. So 5 can't go to 3 and 4.
 [/INST] Assuming you do multiplication left to right, then
$$(3\quad2\quad5)(2\quad5\quad4) = 
\begin{pmatrix}1&2&3&4&5\\
1&5&2&4&3
\end{pmatrix}\begin{pmatrix}1&2&3&4&5\\
1&5&3&2&4
\end{pmatrix} = \begin{pmatrix}1&2&3&4&5\\
1&4&5&2&3\end{pmatrix}$$
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