Current boosting problem with 78xx
Very likely the 7805 is oscillating.  100 nF is a rather skimpy capacitor on its output.  Also, make sure it is low ESR and physically close to the 7805 so that there is little inductance in the wires to and from the capacitor.

I'd make both caps at least 1 &micro;F, maybe even 10 &micro;F for the input cap.  At low voltages, such values are cheap and readily available, and the same size as the 100 nF cap.

Added:

You should also decrease the resistor.  Make it 1 &Omega; or 1.5 &Omega;.  As it is now, the transistor is kicking in rather early.  You want a decent current thru the 7805 when the transistor starts adding more to the output.

There should be no need for a quiescient load resistor.  A properly connected 7805 is stable at 0 output current.