5 is a very high aggression factor and would be a major factor in how I'd be thinking about this hand.
As you point out though his 3bet % is only just over 2 which is QQ KK AA and AK. QQ against this range is 40% preflop and we will be out of position, not an enticing spot. I don't think 4 betting against this range is a good option here so a call looks right.
It is realistic to think however that he might be a bit wider 3betting as he is so aggro. He has 127 hands which isn't anywhere near enough to cement him to QQ+, he might just have a poor run of cards or just not got his good hands in the correct positions to 3 bet.
I also though don't like this odd sized min 3bet which in my experience at these stakes is AA and KK just pot sweetening a bit and hoping not to chase off too many hands.
In the worst case realistically we are facing is 16 combos of AK and 12 combos of KK AA.
So 40% the time we have 12%
equity and the other 60% when he has AK and only has 12 outs we have 75% equity.
It's really a simple maths problem.
My equity calc against his strongest range shows us with 47% equity after the flop. Clearly a bit more than that if we start widening his 3bet range to include TT+ and say AQs when we move up to about 55%
So now the flop is done and decent for QQ its still little more than a flip.
Against a normal player someone with AK might slow down on the turn but I don't think a guy with an AF of 5 will, I'd be expecting him to fire 3 barrels. It's a tough spot for sure so what can we do?
We have the option to raise now on the flop, to call or to fold.
Raising on the flop is likely to fold out everything we beat and we get called by what beats us. This gives us a chance to withdraw from the hand if we get called and not get stacked. The bad part of raising the flop is we stop him from barreling his AK, TT AQs which if they miss then we stack him.If we decide to call him down we just have to accept that just under half the time we are going to lose our stack to AA KK. There is the saviour of being able to fold if an A or K arrive on the flop or turn.
The 3rd option was to fold, this is clearly wrong after this flop. If we were going to fold it should have been preflop which is too nitty to even contemplate.
My play...call him down, give him the chance to 3 barrel the hands that are worse than ours and folding if an ace or king hit turn or river. He has was a tight or more passive player, we can more happily fold if he bets the turn or river for value.
Look at it his way if you have QQ and he has KK or AA you are supposed to lose money when the flop has undercards.