iPhone reboots itself while connected to computer

[Faize]

Over the past week or so, I've been having a strange issue where my aging iPhone 5 will sometimes - but not always - reboot itself shortly (10-30 seconds?) after the screen turns off if the iPhone is plugged in.

I attempted to restore the iPhone just now, but that didn't help at all - in order for the restore to even complete, I ended up having to press the Home button every couple of seconds throughout the whole 5-10 minutes it took for the restoration process to complete, otherwise the iPhone would reboot itself and the restore would fail. It almost felt like I was doing CPR on the iPhone

 

[Bomb Bloke]

That sounds like some sort of really weird grounding issue - as if one of the two earth pins in the USB lead were damaged?

Try a different cable / USB socket, it may be as simple as that.