Stepper motors (as are nearly all electric motors) are thermally limited - try
driving via a L293D at 5V supply and see how hot the motor gets. If its too hot
to touch its probably too much, if its just hot that's likely perfectly normal. These
motors focus digital cameras and are intermittent duty rated, not continuous. Expect
about 100mA for a 20 ohm winding (I've some with 50 ohm windings and they
need more than 30mA - so I can't run them direct from Arduino pins alas (with
diodes of course).
I suspect 20 ohm windings are designed for 3.3V, 50 ohm for 5V, both give 0.5W
to the motor winding.