In the PLC-5 family, Series letters designate different hardware.
A Series C controller can accept only higher firmware revisions (also letter or letter.number) of firmware for Series C controllers.
I do not know if the firmware for a Series C controller must be installed as a physical PROM plugs, or if some of it can be loaded through the serial port.
PLC-5 controllers could not recover as gracefully from interrupted firmware downloads as ControlLogix can, so it is very important to perform upgrade operations on a stable and reliable bench top installation.