If your stack does not allow you to go through 5 rounds of the game at the table, given the increasing ante and blinds, then it is short. Choose a convenient moment and more or less decent card, it is desirable that in the game there are no more than two players, and go all-in.
Depends on the structure of the tournament, for instance in a turbo or hyper turbo tournament 5bbs is borderline [for me]. In a regular speed 10bbs is borderline for me but you should be alerted an try to find pushing hands even from the ~15bbs and reshoving hands even for the ~20bbs.
As for the range for the above actions I would recommend searching the internet instead of just write you down my range of hands. There are plenty of pretty decent push/fold charts
It also depends on the stage of the tournament, tournaments speed and number of the players at the table.
On the final table you can push much more hands, but remember you can always have a bad luck, when you have AQ and your opponent AA for example, that happens.
Usually I go all-in preflop with monsters in the late stage of the tournament, even with +20BB, cause QQ is not so safe to slowplay and someone with A8 can check low raise and get Ace on the flop.
Go all-in with pocket pairs and AX. Less stack = lower pocket pairs and X.
If tournament is low speed and it's a bubble/late stage you can wait for good hands even to 5BB.
10-15BB reg speed and 5-6BB hyper or turbo. shove any pair 88 and up and A/10+ suited connectors 9/10+. Have to remember that if someone opens ahead of you, even though you are in push fold, unless you have the top 30% of push hands, you want to consider a fold as they are prolly ahead. if it folds around to you, then you can push with anything stated above.