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.
Do the actors' physical changes need explaining at all? There is no real justification for the complete change in visual aesthetic between TOS and the movies either, except to say the producers changed and updated how Star Trek looks. An Enterprise refit doesn't cover the complete change in the Klingons, for example. Or that not a single computer console, keyboard layout or screen readout in any way resembles those seen in TOS.
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.
But in TMP, everyone's active and it ends with them warping off to new adventures (the apocraphyl second 5-year mission - after all, TMP began life as the pilot episode for Star Trek Phase II). Then, in TWOK, the crew are split and those remaining are in the twilight of their careers, training the next generation of Starfleet. They only reunite on the Enterprise for "a little training cruise"
Back in the old Best of Trek
books, there were fans who believed TWOK deliberately ignored TMP, and others that felt the movies were incompatible.