I understand that "the only thing that is canon is that which is shown onscreen" but I don't think that means that 'canon' cannot include reasonable inferences based on what *is* shown on screen. I don't think it is plausible to say we don't know if the Enterprise embarked on a mission after the events of TMP.
You didn't read my post above. I was not objecting to the idea of a mission after TMP; I've written multiple novels and novellas set in just such a mission. I was objecting to the kneejerk assumption that it had to be 5 years long.
In my post-TMP novels, I did accept the conceit of a second 5-year tour, but only because I was staying consistent with Peter David's The Captain's Daughter, which had established that to be the case. I clarified that 5 years is not a mandated duration but merely a recommended maximum service period between refits and crew rotations, so that a ship's mission might well be longer or shorter. I also established that after the second 5YM ended, the Enterprise was assigned as Admiral Kirk's flagship, under Captain Spock's command but occasionally going on special missions commanded by Kirk -- such as the mission we saw in TWOK where Kirk took over to investigate Regula I. (Which is what the term "flagship" actually means, a ship attached to a flag officer and used as their command base, rather than the vernacular use of the term from TNG onward as a ceremonial designation for the "star" vessel in the fleet.) That allowed me to break free of the rigid 5-year paradigm and do something more creative.