Using a separate power supply?
Here's a tutorial from Sparkfun that shows how to drive an LED using a transistor to switch the LED. Where the transistor is connected to +5v, that should be to your external 5v supply. The pin labeled "Control" is connected to one of your Arduino pins. Connect the external supply's ground to the Arduino's ground.

Done this way, the Arduino's pin driver only needs to supply enough current to switch the transistor; the current to power the LED is provided by your external power supply.