Your car can't really run at 5-PSI... if you were really getting 5-psi, you'd have significant lifter clatter, even when sitting at idle.
What you're experiencing, in my opinion, is likely a failing oil pressure sending unit.
Here's a diagram from the Fiero Store:

The oil pressure sending unit is the one circled in blue. You will want to replace this... but MAKE SURE you buy the correct one. There are a lot of oil pressure sending units for sale on places like Rock Auto, etc... and they are these tiny little "sensors." Those are not sending units, those are "oil pressure switches," often mislabeled as a sending unit. The sending unit is the big one that you have, and that allows you to power an oil pressure gauge. The small ones are binary... pressure YES or NO.
Be careful when you unscrew that oil pressure sending unit, it's mounted to a steel block which is connected to a tube which is notionally mounted to the side of the engine. What you'll want to do is get a crescent wrench where the open end will fit perfectly over the block that the oil sending unit is screwed into... use that to hold the block STILL... and then use another crescent wrench (13mm I think... I can't remember) to unscrew the sending unit.
Note, even though the sending unit is super big and looks like you can put a big wrench on the plastic part, you'll really just destroy it... so unscrew it from the metal part at the tip where it screws in.
This is what you need to buy:
https://www.rockauto.com/en...info.php?pk=11762449