"Calcio a 5" is the actual denomination of the discipline, while "calcetto" is the popular term for it. The word "calcetto" has indeed the disadvantage that it does not specify how many people are on the pitch! It can also be confused by some people with the table-football, the so-called "calcio balilla"; indeed my granma has made that mistake many times!
In the end, I would suggest "calcio a 5" because it is as accurate as the word 5-a-side.
Also, I have heard 8-a-side football being sometimes called rather informally "calciotto"..which is quite a funny word to me!