Neon tetras are extremely active, and should be in larger groups... In a 5 gallon, they would stress out the betta with their fats movements - much like danios. Plus, that is a lot of bioload (fish waste) for a 5 gallon. I've also seen some videos on youtube, with a betta and three guppies in a 3 gallon... It's not a good idea a lot of the time. If you had a 10 gallon, I'd say go right ahead with neon tetras - most of the time they get along anyways. Just, don't want to stress out your betta :)
Breed for the breed, not for the money; the words any REAL breeder would understand.
You must know nothing in order to know all, for all is nothing and nothing is for all.