The only mention of the Enterprises age is in TSFS ("The Enterprise is 20 years old") and it is hard to reconcile with other data points.
Here, I'll admit to having to fudge, but I always though Morrow was talking about the age of the Enterprise
since her refit (which would be fifteen or sixteen years) and rounded up for emphasis.
Except it must a lot less time than that since the refit seen in TMP.
TSFS happens maybe weeks after TWOK, which happens approx 15 years after Space Seed. Space Seed was in the first year of the 5YM (assuming a season = a year and season one is year one). The refit was launched to intercept V'Ger 2.5 years after the end of the 5YM.
Year 1 - 5ym starts, SPace Seed
Year 8 (or 7.5 to be exact)- Enterprise refit launched to intercept V'Ger
Year 15 - TWOK/SFS
So, by this reasoning, the refit was only seven years prior.
In my head I always either pretend Morrow said "30 years" or "40 Years" or that the annoyed look Kirk gets isn't just about the decommissioning of the Enterprise, but also because his old friend, the Starfleet CO doesn't know what he's talking about.