They gave us the number in TMP.
They don't, though. (I want to play the petty pedantry game too!

They tell us it's been two and a half years since Kirk became Chief of Starfleet Operations.
TMP doesn't say this happened the instant the TOS 5 year mission ended. It would make sense that there'd be a period of time in between the two events, possibly spent with Kirk as a Commodore learning how to be a staff officer, or with Kirk as a Commodore in command of a squadron of ships.
The movie doesn't say that such a thing did happen, but it also doesn't say that it didn't, so there's plenty of room for 4, 5, or even 9 years between TOS and TMP.