If we assume that the 3 seasons are just the first 3 years of the 5 year mission, we can then assume that something interesting happened only 79 days (roughly) out of 1,095. Coincidentally, those 79 days were when we had the TV on.
Didn't The Paradise Syndrome occur over an approximate two month period?
Yep. And sometimes significant periods of time pass during commercial breaks and between log entries.
"Captain's log. After 72 hours at Warp Six, we have finally arrived at Gamma Beta Regula. We have not received any further distress signals from the colony for over sixteen hours . . . ."
I've always assumed Kirk tried to get some sleep in during the 84.321 hours the Enterprise is en route to their destination. But, yeah, nothing exciting ever seems to take place during the swing shift . . . .