What can I use to turn on a circuit at 5V?
An SCR won't do what you want - it will naturally drop about 1 volt across it when connecting the supercap to the arduino so 5 volt in becomes 4 volts out to the arduino. I'd consider using a buck-boost regulator where the supercap (and charger) is on the input side and, the output side connects to the arduino: -



Vin can work from 2.5 volts to well over 5 volts in so you can choose, if you want to activate the arduino at voltage lower than 5 volts.

How is this activated?

The "RUN" pin is connected to VIN by a potential divider and only when VIN rises above a level determined by the potential divider ratio does the RUN pin activate the buck-boost regulator. It's called under-voltage-lock-out.