Sounds to me like the OP is over swinging on par fives. Trying too hard, so to speak. Playing the 5s differently than the 3s, and 4s due to the longer yardages involved.
I might suggest thinking of the 5s as just a longer 4. Anything to approach the 5s like the other two shorter holes as far as the mental aspect goes.
I know when I play a 5, most of the time I go with 2, or 3 easy 3 wood swings. A close wedge stroke, and 1 putt for par.
The averages posted on the 3s, and 4s suggests that the OP has a decent full swing, shorter swing, and putting game. Perhaps just taking it easy, and getting on the green in 4 on those 5s, will save a stroke. Write down a 6, instead of 7 for now, while working towards writing down a 5.
The way I play, my anti-handicap would probably be 10-15 shots higher than my handicap. Since I started playing again after getting my shoulder fixed, I've played what can only be called schizophrenic golf.