You could probably add a small snail. I’m not sure about shirmp, but I wouldn’t add another fish of any kind. There’s just not enough room in a five gallon to safely cohab other fish with a betta
Very few fish are happy in a 5 gallon, and certainly not sharing it with a betta.
Shrimp are iffy. Bettas will either ignore them or rip them apart, and some shrimp (anything sold as “ghost shrimp” is suspect) will attack betta tails. Same goes for dwarf crayfish- either the betta will attack them or they’ll go after betta fins.
A small snail would be fine, but that’s about it.