The reason I want to try this is because I need to power a digital panel meter (19.99 volts) for my variable supply, it is a "common ground" type. It requires 5 volts, so I can't power it from the variable output of the supply because at times the output voltage could be too low to run the regulator.
I tried powering the meter from a 7805 tapped in to the unregulated input to the variable power supply, which worked fine unless the power supply's voltage was adjusted above about 11.5 volts, then the panel meter's reading would begin to start jumping around and became unstable, and even when the variable output was adjusted to maximum (19.9 volts) none of the meter's readings were over 13 volts. It seems maybe common ground mode is not too happy with too much differential voltage between the meter's supply and the voltage being measured ?
The meter works perfectly reading the power supply's output voltage if it is powered from a separate 5 volt bench supply, all the way up to 19.9 volts the readings are correct and stable. Because of this I thought to put in a separate supply for the panel meter, but there is no room for another transformer. The meter uses a maximum of 75 ma, so I could build it a tiny regulated supply of its own powered from the same transformer, and maybe get enough isolation to get rid of the unstable voltage readings.