5 V, 3 A to 5 V 3 A current limiter for DC motor
The 3 A rating is probably the maximum running load. Starting the motor will require a much higher current.

If you still have the lab power supply you can run another test and this time record the voltage output of the supply while the motor is drawing 3 A.

I think you will find that the PSU is causing the motor to start in current limited mode which will cause the motor to run at constant torque. If the motor can accelerate to running speed then the PSU will limit the voltage at 5 V and the motor will run in "constant speed" mode.

With the motor disconnected you should also measure the motor resistance. From this you can calculate the starting current.

Update your question with the results and further answers will follow.