Re: What do we know about the years between ST5 and ST6?
FWIW, DC's comic series of the 90s had them more or less on another five-year mission. Works for me.
I believe the original TUC script contained dialog more clearly suggesting (or at least intimating) that the crew was basically puttering around before standing down. I believe the thought that Uhura was teaching comes from her mentioning she's "supposed to be chairing a seminar." That of course doesn't explicitly mean she was teaching.
IIRC, there were scenes written where Kirk goes out and rounds up the rest of the senior staff for the mission.
"If I hadn't tried, the cost would have been my soul." - Admiral James T. Kirk, Star Trek III: The Search for Spock