Grumpy_Mike:
I think I have noticed that when +5V is provided on the 7805 output pin, ~7.8V seems to present at its input pin
No that is not only wrong it is impossible. You can't get more voltage than you put in with this kind of circuit.
Right, that should've been obvious 
. Now I recall that that happened when I provided +9V on the output pin.
Thanks again!