You CANNOT use a SN754410 to drive a 5V stepper motor successfully.
The output circuit looks like this:
The output high and low includes two Vbe drops in it, so from your 5V supply at least 2.4V is lost. Driving the stepper motor with only 2.6V is unlikely to work.
You would have to raise your VCC2 to about 7.5V to get it to work. You may be better in raising the voltage to 9V and include a series resistor to reduce the current to the rated value.
Your motor has a 120 Ohm winding (I assume half winding), so is rated for 42mA @5V. If you raise VCC2 to 9V, and use a 33 Ohm series resistor for each half winding you'd get about the right current flow. The higher aiming voltage will give you slightly better pullout torque during switching.
NOTE that in the lab you point to, they connected the motor supply VCC2 to 12V ….not 5V.
You should test your winding current by connecting the center tap to +5V and one of the endpoint windings to Gnd. Whatever that current is will tell you the resistance of the half winding