It should work as long as the mechanical load is not too high and you always start with the motor speed at or near zero.
The motor is rated 5A continuous at 5nm torque, with max torque figure or 25m - so presumably a stall (= full speed start peak) current of 25A or higher.
I'd be tempted to go for a rather higher current rated PSU, so it has a better chance of handing starting surges and the running current is a lower percentage of its full rating.
That may also do better in a smallish enclosure.
You can run the PSU from the same power inlet, I'd just add a fuse near the PSU in case it ever has a problem.