They CAN...but...Personally, for a 5 gal I wouldn't put anything else in with the betta except for something like some little Pygmy Corydoras cats (Corydoras Habrosus), shrimp, or a snail or two. Bettas don't like things that swim in their "space," and while neons and bettas normally can get along, I've seen them more prone to getting into fights with each other in anything smaller than 10 gals.
Small catfish, snails, and shrimp are good choices.
Though this will also depend on your betta's individual personality and whether they will ignore or attack. Some bettas get along with most everything, others will attack everything. My last betta was too aggressive to tolerate anything at all (he would even attack snails!), so he had to live by himself. He liked to attack my finger regularly. My current one is pretty mellow and does fine in community tank setting.