Sharing a power supply between arduino and led strip?

RobertPN:
My question is, why can't they both share the external psu?

They can both use the same PSU, no problem. If it's a 5V PSU then simply connect the 5V from the PSU to the Arduino 5V pin.

nb. Make sure it's a regulated (switching) supply with exactly 5V. Don't try to connect the USB cable at the same time or anything like that. Connecting two PSUs together is bad, mmmmkay...