Q5s

If button was 100bb deep, I think you can call.
But as he is very short - I am not ok.

Short = broader range, but still, probably ahead of Q5s, would definitely let it go. Not an expert tough.

chasing down flush draws gets expensive.

The problem in this spot in my opinion are 3:
1. BTN OR range has you covered.
2. He is very short stacked so you are not getting very good implied odds if you hit a flush draw.
3. You are going to play OOP.

Having said that if you know beforehand that this player folds enough postflop you could call. Or the same way if his fold to 3bet is enough just 3bet him.

This is a border line situation. Normally I might call but since BTN is short stacker our implied odds get worse, so this could be folded. Also calling a weak suited hand like this requires some postflop skills because a mistake postflop with this kind of hand is a lot more expensive than a mistake preflop.