Mr. Scott's Guide to the Enterprise
Therin of Andor wrote:
IIRC, the TMP novelization says something about the Enterprise being the first of its class to return from a 5YM with the ship and its crew "relatively unscathed"
goes one further, and says Kirk's Enterprise was the only one of the original 13 Constitution-class ships to return at all
. Shane Johnson uses this to justify the Enterprise's extensive refit (she and her crew are famous now) and the Enterprise emblem being adopted fleet-wide.
Yeah, I have a feeling by the time we get to STID there is probably very little that is the same between the two universes.
Unless you read the comics, in which case a bunch of TOS' 5-year mission missions happened years earlier and before this new Enterprise's 5YM.