Hero running 30/25/13, Villain running 24/16/31.6 over 37 hands. Blinds 75/150/15. Currently 7 handed.
UTG opens to 390, CO calls, Hero in SB raises to 1375 with Q

Q

UTG calls, CO folds.
Flop is 5

9

9

Hero bets 1400 into 3400, UTG calls.
Turn is A
Is this a bad spot to shove 5k into 6.2k repping Ax?
Given his preflop flat, villain's range may not include many Ax combos (4b shoving AK, blockers to AQ, AT-AJ folds a bunch). Is his range more weighted to pp's and random floats? Should I expect a fold from AT-AJ sometimes on the turn? If I check the turn I feel like I have to c/f the turn/river and I'll rarely get to showdown unless vs a pp that's folding to a turn shove anyway.