Yes it is possible to cycle a 2.5 gallon, I did it successfully and carried our 50% water changes twice weekly

I kept RCS in the tank and none of these died, thankfully
Basically what you will need to do is set the tank up and let it run

I cycled my tank by feeding the tank a few flakes of food every 12 hours, or you could use a piece of raw fish or shrimp. Usually a tank will take about a month to fully cycle but for a quicker way you could add substrate, decorations and filter media from an already estabilished tank, it took me a week to cycle my 6.5 gallon tank this way. If you have the API freshwater master kit to test your water, when the parameters read
Ammonia - 0
Nitrite - 0
Nitrate - 5-10
Then your tank is cycled and its safe to put in fish but usually a water change is recommended before adding the fish to rid of any high nitrates

This is just a basic guideline from my own experience

the 5 gallon would probably be better as it is slightly bigger and bigger is always better
Another thing, do you use water conditioner with every water change?