How to achieve better infrared transmitter performance?

I have wired up an infrared transmitter using a Teensy 3.1 and a raw IR LED. The anode is connected to pin 5, running through a 47 Ohm resistor, and the cathode is connected to ground. I'm controlling a Raspberry Pi wired to a typical IR receiver, running LIRC. It works pretty well in low light (consistent results from about 10 feet away), but with all the room lights on I need to be within about 4-5 feet for the remote to work. This is poor compared to any off the shelf IR remote control.

I assume it's a current issue, since the Teensy 3.1 can only output 10ma on pin 5 but the LED is capable of 100ma when pulsed. I plan to run the LED on a 4-5 foot cable away from the Teensy too, so that will further degrade the power. Any recommendations? How would I drive the power off the 5V supply using pin 5 just for signal rather than voltage supply?

a) Teensy-Pin -> 2.2k Resistor -> Base of 2N3904
b) Emitter of 2N3904 -> Ground
c) +5V -> IR Anode and IR Cathode -> Collector of 2N3904

Thus there will be only flowing 1.x mA out the Teensy to drive the transistor. The transistor is then capable to drive the IR LED with full current. It will (depending on the IR LED) be necessary to add a current limiting resistor between the IR LED and the transistor's collector to avoid exceeding the 100mA peak current. I'd start with 47 Ohm and then lowering this value successively.

Great! Thanks. That should be perfect.