Correct Voltage Detection
You could look into using a TL431 adjustable Zener diode along with a P-channel MOSFET with low threshold voltage.  You can also add a single resistor to provide a little hysteresis.

Look for a class of MOSFET called "trench FET".  These have very low gate threshold voltage.

I'll sketch something out but won't have a chance to see if it actually works.  But you can either simulate it or build it.

Pick the voltage divider resistors to turn ON at somewhat more than 4.7V.  Maybe 4.75V or so.  This will drop slightly when you add the hysteresis resistor.

Sketch follows:







simulate this circuit &ndash; Schematic created using CircuitLab

Resistor values shown are (very) approximate.  You will need to calculate the proper values yourself.

MOSFET part number shown was grabbed from Digikey.  It is rated as having RDSon max of about 0.1 Ohms.  Choose a different part if you need better than that.

You can choose whatever value of hysteresis you want simply altering the value of R4.  Do note that the value of R4 affects the threshold voltage slightly.