Welcome to the forum!
Though bettas are quite hardy, many come from the store already in a sorry state due to being in those tiny unheated cups. I think the humane choice is to do a fishless cycle. It's also a lot less work for you because you don't need to do water changes during the cycle like you would if you were cycling with fish (in a small tank like that, you can expect to have to do water changes at least every day during the cycle to keep ammonia/nitrite levels down if you cycled with fish).
Some other fish ideas:
-A school of tiny fish like galaxy rasboras
-A few Endler's livebearers
-A single betta, as was mentioned
-A pair of sparkling gouramis
-A single or even pair of scarlet badis
-A single dwarf puffer
-If you got a standard 5.5g, maybe a pair of dwarf shelldwellers
-Some of the smaller killifish could work well in a 5g tank
These fish have different requirements in terms of care and water chemistry, so I suggest finding out your water's pH and hardness before settling on any fish in particular and then choosing what sort of fish you want.