Problem is in canon we don't exactly know when the TOS five year mission took place, which years. That part is loose conjecture.
Between the time the Enterprise returned to Earth and the events of TMP, up to a decade easily could have passed.
Even if the 5-year mission ended in 2270 (by the way, in my personal continuity, TAS was the 5th year in '70), there's no writing on or off screen to explain the physical changes of the characters
(actors) from "Turnabout Intruder"
to TMP. As in real life, we witnessed the actors grow older throughout the 1970s, on par with the near decade of time between TV and film production, so the only rational explanation cannot have less than six, maybe seven years of time passing to sell the characters' physical appearance.
Still I think canon must be forced into accepting a ten year gap between TV and TMP, as Kirk sets a fixed date in TWOK, when he tells Carol he had not seen Khan in fifteen years
, which--considering the real life 1967 airdate of "Space Seed"
to the 1982 release date of TWOK--is exactly fifteen years. There's not much phyisical difference between the actors from TMP to TWOK (aside from Doohan gaining a few extra pounds), so we have to assume TMP occured only a few years earlier---probably three.
If that's the case, then any published dates of TMP occuring a mere 2 years after TOS cannot be taken seriously.