Am I drawing too much power from the board?

DrDiettrich:
PieterP provided useful circuit diagrams.

The first diagram would work, but the base resistor in the first diagram should ideally be 1k to saturate the 2N2222/BC337 (between 1:10 and 1:20 base:collector current).
The second diagram won't work, because four LEDs have a Vf of 4*~3.3volt = 13.2volt.
Three LEDs and a 100ohm resistor per string would work.
Base resistor should be calculated for 1/10 of collector current for saturation.
Ic = ~40mA, so Ib = 4mA. R = (5volt - 0.7volt) / 0.004Amp = 1075.
A 1k base resistor would do.
Leo..