I have the same problem and am watching this thread hoping to see a fix. My 99 manual 4.0 also reads 5 psi no matter what, just like the OP. To add my experience to other posts, I have the original ECU in the jeep and it runs like a top with no issues whatsoever. Prior owner installed a mechanical oil gauge and oil pressure is running in the proper range. Also, I have tried the mopar sender as well as a number of aftermarket units with no difference.
To the OP, I don't think it's the ecu if everything else runs fine. The fact that the oil pressure gauge needle moves at all when the ignition key is turned on means that the Jeep is getting SOME signal from the sender (a disconnected sender will show a dead gauge). As to recommended fixes I am stumped at this point. I toyed with the notion that either (1) the instrument cluster was swapped by the prior owner and is not compatible with the sender (2) there is a frayed wire somewhere from the sender to the instrument cluster which is not allowing a full signal to the cluster, or (3) a loose connection behind the instrument cluster. Due to laziness I never checked on these things.
Maybe check on these things related to wiring or the cluster and let us know if that fixes it.