A stalled DC motor looks like a dead short until the rotor begins to move and starts making a back emf to reduce its current demand.
The stalled current can be a factor of 5 higher than the running current, so your 5A motor might draw 25A from the power supply for several ten of ms while the rotor starts moving...
25A can pull-down the voltage on the power supply until the motor starts. One method is to put a series diode going to from the 12V supply to a (new) large electrolytic filter capacitor, and put that in the path to the voltage regulators. As the supply is pulled down, the diode blocks.
That way, even if the in-rush to the motor pulls the supply voltage down to 3V, the regulators simply draw off the energy stored in the electrolytic capacitor until the motor comes up to speed, and the supply recovers. See below:
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