Tetras typically are stressed out if in groups less than 5. A small school of tetras would not likely do well in a 5 gallon tank with a betta. Bettas like to have their own space and may become aggressive towards any fish that invade his territory. Plus your tank is rather bare - when my neons are feeling threatened, they always tuck themselves into the silk plants to feel more secure. With all the open space - there's no where to run and hide if the betta becomes aggressive.
Keep in mind, the fish may "fit", you have to keep behaviour and the bioload in mind. If you exceed your bioload, you will have a large ammonia spike in your tank which will harm all fish in the tank.
Check with aqadvisor.com if you are unsure if your tank is overstocked. IMO, 1 betta and 5 neons would be overstocking the tank.
Last edited by Sathori; 05-01-2014 at 08:52 PM.