you could do this with JustAddPower.

a transmitter would connect to your source at the head end.  then your cat5 would run to the tv and plug into a gigabit network switch.  from there you would plug a JAP receiver into the switch and wire the hdmi to the tv.   you would have another cat5 plugged into the switch and run over to the projector.  you would install another JAP receiver at the projector and plug in the Cat5.