First, hello and welcome to the forum.
Unfortunately, 5 gallon isn't very big and really limits what you can have. The people that told you 1 or 2 are closer to correct. I have a 5 gallon tank with nothing but one male betta in it. The general rule of thumb for beginners is 1" or adult fish per gallon of water. That would pretty much limit you to about 2 or up to 4 small tetras.
I mentioned them in my first post bt as mentioned, they do prefer groups. Neons are fairly small so you could possible hae 3 or 4 of those but they need good water conditions so you definitely need to do a fishless cycle.no1 mentioned how many tetras i could havelol