How does villain see you? Does he think you could be 4-bet bluffing?

I don't think he has KK+ because he didn't 5-bet shove. If he has an ace, of course he's never folding, but I don't think he has an ace all the time. Against QQ, JJ, AK and AQs (of course his range could be wider), you're 54%. Say he folds QQ and JJ when you shove, that's a third of his range and you're 35% against the aces he calls with. So, if you did shove (just checking out the EV as a benchmark), you win 11 a third of the time, and two thirds of the time, you win 26 a third of those times and lose 15 two thirds of those times, for a final EV of about $2.80.

So, even tho shoving rarely gets called by worse or folds better, you have alot of equity in the pot right now, and I think you should shove to capture it.