For a House supply oops (EDIT)
As for Solar power back up, I would get high wattage solar panels and charge up a battery bank (think car batteries) and run a 120VAC inverter on it. Not very descripitve, but should point you in the direct direction.
FOR YOUR CIRCUIT Seeing that it only draws 20ma at 5V, lets make it safe that it could for what ever reason start to want 50ma. I would get a 6W solar panel (12V 500ma) and run that into a 5V regulator. That should work great, and for night time put a 9.6V battery or whatever voltage would suit it and attach that across the input voltage (12V solar panel) and ground it electrically to the solar panel. Make it a NiCd or NiMH. This is just a vague suggestion, I would wait for some of the other pros to state their opinion too.
i would def go for batteries meant for use with solar panels, cos car batteries are ment to have large amount of power drawn from them and are not so good for long "light" discharge
You can eailly trickle charge the batteries at C/10 using a simple series resistor and schottky diode, to prevent them from discharging back into the solar cells.