It isn't about the amount of gallons, well that is part of it... Anyways it depends on how much of a footprint the tank has. I have seen the 5.5 gallon glass tanks. If it us one of the glass tanks then no to fish. Your betta is territorial, no matter what you believe, he needs his space. If you do get shrimp you need lots of hiding places for them like mosses or small caves. Either ghost shrimp or cherry shrimp.
Shrimp are very sensitive to water parameters, how long has your tank been setup?
15 Gallon NPT
1g no tech bowl in the making