I don't think they made indexed 5 speed derailleurs, so you may be mistaken about the shifter- unless it is just ratchet clicks, and not 4 specific clicks between gears. If it is the latter, it would have to be for an S-A IGH hub.

When I was a kid, I had a Ross Apollo 5 speed with a stick shift- it was not indexed- it was a ratcheting shifter. I can't remember if it was a Shimano or SunTour RD. Grey hair eats memories...