yesterday I was playing a live tournament. We are on the bubble and I am in the small blind with 3BB. This is a satellite, so everyone get's the same prize post bubble.

Everyone folds round to me, and I have K5, big blind has an average size stack and calls turning over K10, I lose and therefore burst the bubble.

what could/should I have done differently?

Easy to say, but considering the structure I would have folded

Depends on whether there were shorter stacks. Probably a push as you seem short and it is the best situation to push you will get.

Easiest shove ever if no one else is in immediate danger, unlucky he had you dominated.

If someone is shorter stacked and at risk of being all in before you then I can find a fold here, but a trivial spot to push regardless K5 will do pretty well against the BB's range but unfortunately he had it this time.

if you are last with chips - easy shove. if there are people behind u (knowing that you will have one free orbit) - easy fold.

You didn't elaborate on the stacksizes of other players in the tournament. Try to reflect on whether you were completely aware of the stack situation or not during the tournament. As pointed out by other posters, this is the single most important factor when taking decisions in satellite bubbles.
If two or more players are going to be blinded out before you do (if you fold every hand), you should just fold every hand. The chances that all of those survive are very slim.
If your stack is shorter than everyone else's, you will have to be lucky at least once with a showdown, except if there are total donks at your table that don't understand satellites and would be able to bust with a comfortable stack.
So if you need to get lucky once, the K5 has fine equity against a random hand in the big blind. So in that case it is definitely a shove.
If anybody tells you to wait for a better hand (again, taking as a hypothesis that you are the next player getting blinded out), don't listen to him. You don't have that many hands left to survive and with 3BBs, you have close to no fold equity, given that we are in a situation where all the other players have bigger stacks than you. So imagine you get Aces in UTG+1 position. There are still 7 players to act. If some of them have comfortable stacks, some of them may very well team up to catch you and your 3 big blinds and if you play your aces (very lucky already!!) against 3 players, you're probably still a 50% to bust. Your K5 is favorite against a random hand in the big blind. So take the shot.