OK, so it's 4.7v not 5 and I think your only chance is to apply that directly to the 5v pin, thereby bypassing the local supply circuitry. There was recent discussion about this and you should trawl for that.
One thing you can be sure about is that, if you are feeding 4.7v into the standard 2.1mm power socket, you are wasting your time. My 5.3v phone charger isn't up to that, and I guess when they say 7v minimum, they really mean it.,