Here is how I would do it: The Sim shows the LED current and LED Vf as a function of the emitter resistor. This method draws less current from the port pin, and has a more constant current through the LED if the 5V supply changes than the circuit the OP posted.
The collector current is nearly the same as the emitter current. Since the transistor is operated as an emitter follower, it is not saturated, and the base current is tiny compared to the common-emitter configuration.
Hey Mike.
Could you explain why this Emitter Follower has its IC more constant when VF of the LED changes?