ATX-PSU to supply PC and RaspberryPi
Read the label on the PSU box. It should say the maximum rating of +5VSB. It is probably 2-3A. So that should be enough for Raspberry Pi assuming it needs max. 1.5A and the rest remains for motherboard.

Why do you need that cable? +5VSB is on no matter if your PC is off. 

That cable either allows you turn on the PSU from an external device, bypassing motherboard commands or allows you to monitor motherboard power on status. 

The green wire of an ATX connector is called PS_ON and when connected to GND turns on the PSU (is active low). That doesn't affect +5VSB which is always on. On older PSUs this voltage was taken from a linear transformer, totally unrelated to the SMPS that supplies the rest of the voltages.