I am no sim expert...

but if the same sim works in another phone..
and different provider sim works on the 5..

there is specifically something wrong with how the 5 is communicating with that sim...
it isn't the sim ...that is for sure.
your 5's memory of that sim's info is the issue.
there is some discrep. there.

Frankly I wouldn't mess with it.
I would reinstall over it fresh, leaving your storage and what you may have in it ..alone..
May be extreme..
but ..if few have experienced such an issue as yours ...
digging around inside not knowing exactly where the root cause is ...
or what parameters exactly to set the 5 back to...
may not be a good idea...