Where can I find a bathroom fan that will fit in a 5" cylindrical space?
I lived in a condo built in the early 50's with a super cool looking chrome bathroom exhaust fan.  The original motor finally died after 54 years of service... so I went looking for a replacement fan/light unit.

Unfortunately I was unsuccessful as well since the original fan housing is not the "standard" (read: newer) bathroom exhaust fan size.

Anyway, I was able to find a replacement motor for the exhaust fan assembly and it worked beautifully.  If the motor has any nameplate data on it - odds are you can probably find an equivalent replacement.

I bought mine from this place Replacement Bath Vent Fan Motors - just remember it doesn't necessarily have to say "bath vent fan motor" in order to work, so long as the motor nameplate data (volts, amps, HP) are similar.

Good luck!