Connect LED-driver (BJT) in circuit
Lets say your LED is rated at 20mA, so I'm picking 10mA over the LED as a nice value that works, If you want it for 20mA then the math is all here

The lazy way that this is seeming to ask is to just have the transistor in saturation, acting as a switch, as such lets say its current gain is 100 (beta), we want 10mA or more to flow between collector and emmitor, so we want atleast 100uA to flow in to the base

5V - 0.7V (transistor base) = 4.3V, 
4.3V / 100uA = 43000 ohms (RB), lets pick 39K ohms as the nearest preffered value that is lower

Now with the transistor acting as a switch, we have 5V, while It does not list the LED forward voltage, I'm going to assume 1.5V, as a common value for a red LED (assuming again), 

We want 10mA, so..
5V - 1.5V = 3.5V
3.5V / 10mA = 350 Ohms (RC), rounded to nearest preferred value would be 330 ohms