I would say so. Neon tetras only get to be about an inch long (maybe up to an inch and a half) when fully grown. Along with their counterparts, cardinal tetras, they're probably one of the smallest species of fish you can get as a pet.
As long as the tank isn't oddly shaped to where it's tall and skinny, which would limit the swimming space inside, I would say you could fit anywhere between 4-6 neons in there. I wouldn't keep less than three because they're a schooling fish and it would stress them out to be alone or in a pair,and any more than six you're better off buying a larger tank to save the trouble of keeping the water clean.
Having less fish in the tank gives you more of a buffer zone in the small tank, to keep the risk of the waste causing an ammonia spike from happening and killing the fish. The downside is that neons are a schooling fish, so the more there are the more comfortable they will be with swimming about in the open.
On the other hand, having more fish in the tank gives you more to look at, and gives the fish comfort with being in a larger group, but you have a smaller buffer in case something changes with the water. It mostly means you'll have to be more proactive in keeping the water clean, performing more frequent water changes.
I'm assuming the neons are the only fish in the tank. Even with only 3-4 neons I wouldn't add any other fish to the tank.
I would make sure any decorations don't take up a lot of space. Keep in mind that it's a 5 gallon tank before adding the substrate and decorations, adding a large castle or volcano will displace water from the tank.