DC/DC Converter Instant Off
I have the feeling, unless I misunderstand or just miss some extra requirement, that you are over-engineering this.

You have a supply that is higher than your backup-supply by more than 0.1V.

Just the diodes will give you the best and quickest response: Leave out the P-MOSFET.

So long as you have a back-up supply that is a little lower than the main supply, you need to do nothing other than have those two diodes. Once the 5V drops below 4.7V the 4.7V back-up will take over instantaneously. Well, yes, there is a transition period, but it's in the order of millivolts for most diode types of the same type and same batch, if not less. I'm too fuzzy right now to do the full maths.

If your back-up is higher than the main supply (this is an exceptionally weird situation, to be honest), you will need a switching element, the easiest way to get that is to use a comparator. They can give a very nice, sharp and hard response on a fixed voltage.

If you have a 2.4V reference and divide the main supply by 2 through a resistive divider, you can compare those with a comparator directly and it will be able to switch a transistor. If the comparator has an open-collector output you can use it directly for your higher-voltage back-up supply, if it doesn't you'll likely need a support-NPN-transistor to translate its output upward to the P-MOSFET of the higher back-up voltage.

But again: Your back-up is below the main voltage, as is very usual, so just the diodes are more than enough.