The NEMA specification dictates the dimensions of the motor, but generally not the electrical specifications. The voltage used to drive the coils on steppers is part of the motor's electrical specifications, found on the data sheet for the motor.
5V is probably not the most common coil voltage for a stepper, unless it's relatively small or weak motor.
There are several stepper motor modules, making use of a variety of discrete components and/or dedicated driver ICs.
Hobby type steppers are often bi-polar, and have 2 sets of coils, and thus you need 2 independent H-Bridges to properly drive it.
Some available driver ICs and modules that use them include:
Allegro MicroSystems' A4988
TI DRV8825, TI DRV8880, TI DRV8834
It should be easy to find boards based around chips like these to drive your stepper from an Arudino.