Olive, you can definitely add more. I had an iridescent shark, a three inch goldfish, and a two inch goldfish in my five for over three months until I did research.

) (they all survived, I gave them away).
If you look at my sig, I've got lots of fish in my 5 gallon, and they've been in there for over a month. I do water changes twice a week and they're fine.
I saw you could get up to six neons (at most) if you do a few more water changes and don't feed them too much. I'm not sure if they eat algae, but if they do you can keep pollutants down by growing algae on rocks and placing them in as an alternative food source.
I would suggest going with shrimp or a frog instead, though, so you can get bottom feeders to clean up a bit and add activity to the bottom.