+1.In my opinion and experience, neons need more swim space than a 5g allows.
+ another one. I don't think bioload would be your problem. I have neons in my 30 gallon, and they love to spread out and explore the entire tank. They are pretty active.+1.
Though it can "theoretically" can work, you'll have a shoal of miserable fish in your hands. Although neon tetras aren't crazy-hyperactive like danios, they still prefer a bit of swim space, with 10 gallons being the minimum.