"So if the increase in health care was 2.7 % in the past year, why are provinces asking for 5.2 %."

Ahh, now there's the rub, isn't it.

The reality, of course, is that most Provinces are fiscal basket cases and they need the extra "health care" funding to reduce their deficits due to all their other spending.

Now, to be fair, some of this is a historical thing going back to the 1980's and especially the 1990's.  During those years total Federal transfers for health care were slashed dramatically, leaving the Provinces to foot the bulk of the bill.  Since 2003 the Feds have been reversing course and we're now back up to funding levels comparable to where they were before the big cuts that happened under Chretien's tenure.

However, as noted above, the Provinces have been breaking the bank on everything, no just health care.  So even though the health care funding is back where it was they are still broke due to all other spending.