How sure can we be about how much time has passed? IIRC the only timeline clue in the movie is Kirk saying he served two and a half years as chief of Starfleet operations, but there's no way to know when that assignment started.
Kirk also says to Decker, "five years out there dealing with unknowns like this", which would indicate there was only a single five-year mission. However, that doesn't preclude Kirk and the Enterprise having an additional mission which perhaps wasn't an exploratory mission (so no dealing with "unknowns", as during the five-year mission). Maybe they functioned as the Enterprise-D seemed to do much more often, as a diplomatic/policing vessel flying the flag of the Federation to various events.
[Note: this just postulates soley from the events of TMP, prior to "Cause and Effect" retconning the red jackets to 2278]