[Lordy]

Interresting spot, I'm gonna try to make some EV calcs (first time I do it for a shove rather than a call, so please correct me if something's wrong) :

EV of shoving :

Board: 7h 7d 5d
Dead:

equity win tie pots won pots tied
Hand 0: 39.045% 39.00% 00.05% 7722 9.00 { 9d8d }
Hand 1: 60.955% 60.91% 00.05% 12060 9.00 { QQ+, AdKd, AdQd }

Assuming his raising range = his calling range :

You invest 136.55 to win 136.55+(2*24.50)+32.50 = 218.05
218.05*0.39-136.55*0.61 = +1.744

So even if he calls 100% of the time, it's about break-even. If he folds just a small % of the time, it's a clear shove.