I have a power supply that shows a slightly higher amp current output than called for. Is there any problem with the current being too high or do you just need to worry about the voltage when picking a power supply?
No problem, a device that is designed to connect to 5V will take as much current as it needs.
You don't worry in your house when you plug in a radio or an electric fire, both take the same voltage but vastly different currents, if this were not the case then your radios would get very hot.
I have a power supply that shows a slightly higher amp current output than called for.
Usually you would want to size the power supply so that the current capacity exceeded the expected load by a suitable margin. It’s not a good idea to have a power supply working right up to its rated limit. So, if there’s a problem it is that ‘slightly higher’ might not give you enough margin.