I broke my fifth metacarpal and my ulna. Can doctors fix both at the same time?

Yes. Unless there are factors we don't know about (infection, etc), both should be able to be fixed at the same time.
Yes. Both fractures you mention can and should be treated at the same time. Treatment may include temporary immobilization in a cast/splint, bone setting, surgery or a combination of all three. The goal is to get the fractures to heal in the best position possible to reduce long term problems and promote early motion exercises in order to get you back in the game as quickly as possible.
Ulna and fifth mc fx. can certainly be fixed at the same time if indicated. Fixation of bone is used to improve and hold position, allow early mobilization and stabilize bones that are not stable enough with casting or pinning closed.