The max current through NP2222 is 650mA.
The max current I can flow with a 5V signal at the base
This statement is wrong on many levels.
The NP2222 works when current (ie. amps) goes through the base, not when a voltage is applied to it.
The transistor has a gain of 100 (or more) so you need to allow 6.5mA (or more) of current through the base. Normally you use a 330 Ohm resistor between the Arduino pin and transistor base for this sort of transistor. This allows enough current to fully turn on the transistor.