HAND REVIEW: QQ facing a 5bet shove

http://www.pokerhandreplays.com/view.php/id/6866591

- villain is playing 20/17/11 over 87 hands.
- we are 10 away from the money, (I'm 10/80, 70 get paid)

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So at first I thought this hand was an unavoidable cooler, but I'm pretty sure it's a mistake now.
A friend's thoughts:

- by 4betting, we are folding out the hands in his range that we beat (AJ,AQ, JJ, TT) and we're committing ourselves against a 3% range. Keep in mind that there is 50bb effective.

Hands I think he might 3bet with:
99+, AJs+, AQo+

Hands he 5bet shoves:
QQ+, AKo+

I'm not even sure that he 5bet shoves AK for 50bb, but even against QQ+, AKo, we are 40%.

- also, 4bet folding here is obviously out of the question because we'd reduce our hand to 72o. We should've called the 3bet and kept his range wide postflop.