I swear I remember reading somewhere that I can't do this, but I don't know where that was and I don't know if I'm wrong.
I've powered an old arduino from a 7805 chip directly to the arduino when the onboard regulator failed to regulate the voltage to 5v via the external power jack. I've read that the uno onboard voltage regulation setup is different and might be damaged if the 5v bus is directly powered with 5v. You might find this info on the arduino site where the uno is described.