I have a power window motor which is powering a rock tumbler and baffled!
Regardless of load, any motor will draw a high current (4X to 10X normal), when power is first applied, before the shaft starts to turn. Depending on motor type, design details and load characteristics, the current will drop to normal in milliseconds to seconds. It is likely that your 2A power supply tolerates the initial current while the 5A supply is shut down very rapidly by its electronic protection circuits. Since it does not appear to be well protected and it is not rated for the expected motor current, the 2 A supply is likely to fail fairly soon if you continue to use it.