Macandmel,
If your A/V box has a wired 12v input then it should output 12v on the ANT IN port. If you haven't done so already, remove the JACK antenna coax right at the back of the A/V box and using a short piece of coax measure the voltage again on the new piece of short coax. Still seeing only 5 volts? If yes, the pass-thru in the box has failed and it should be replaced. If you do see 12v now then I might suggest replacing the cable connector ends on the existing coax to the JACK antenna. It's very common for the roof-side connector to become corroded internally and the voltage becomes erratic.
If the A/V box pass-thru has failed, in lieu of replacing the A/V box you can always install a winegard power supply for the antenna. You can safely cut the 12v wiring from the A/V box and use those as supply wires for the new power supply. You A/V box only needs the 12v for antenna booster power. You can surface mount the wall plate using an electrical box of some sort, or flush mount if you want do some cutting.. your choice. This is a picture of the standard power supply:
Linear Mode
