When I have AQ, I ask myself this, would villain ever do this with AQ/AJ/AT? So you are left with the following range:
AA, KK, AK, and MAYBE QQ and JJ. Aside from JJ, you're in a lot of trouble vs. villain's 5 bet shoving range. Unless they are completely nuts and are doing this with a small pocket pair, you're not doing well.
Just out of curiosity, are you playing Zoom on Stars or Snap on 888
? Or just a standard ring game where your opponents don't change? It sounds like you don't have a read on the villain here.
I've learned to fold AQ if I am 4bet against, and just auto fold if I'm in late position and a raising war has started in front of me.
Maybe that's a bit on the nitty side, but I'd rather be initiating aggression instead of reacting to it.