A Hypothetical Situation:

Assume you are the big stack in a NLHE game.
A short stacked player with 10 x the Big Blind raises to 5xBB from UTG.
2 medium stacks call, and action is to you on the button.
You are fairly sure from your reads that if you push, the blinds will fold, the short stack will call all-in, and both the medium stacks will fold, leaving you heads up.
There is 16.5xBB in the pot.

What is the minimum hand value that you need to make this play?

How does the correct play change if this were a tournament, instead of a cash game?

What hand would it be correct to just call with?

In a cash game, you better have the goods or else you're throwing away money.

In a tournament, if you know you can get it heads up Q7 or better will do... This is strictly based on the WPT notes saying Q7 is the average hand heads up. I would always want to do it with at least 2 big cards

If a short stack does not go all-in, but only raises, they probably have a monster.

I need a read on UTG but assuming he's a decent player I'd say QTo or better if I feel like gambling. If I pushed with that I'd expect to be about a 2:1 dog going in. If I'm looking to be ahead pf I'd need AKo or better here - short stacks putting in only 1/2 their stack utg = monster.

If I'm the big stack in a tourney and it's the final table, I put him all-in with almost anything.

I usually won't mess with this unless I have a hand like AJs or better or pocket 88s or better. Basically, I have to have a hand that I don't feel like folding. In my opinion, trying to make a move here is asking for trouble. It's not as if you can win the pot outright. You will still have to draw.