A couple of questions on the 2N2222 transistor

Look at the On Characterics on sheet 2.
With Ib of 15mA, the base-emitter voltage will be ~0.6V and the collector-emitter voltage will be ~0.3V.
Use those numbers to work the resister values.

(5V - 0.6V)/15mA = Base resistor
(5V - Vf - 0.3V)/20mA = LED resistor.