Does 12v 5A power supply is okay to operate motor shield external power I am new to arduino.

Recently purchased motor shield V1.0 which have two l293 and can run 4 DC motors simultaneously.
But here the problem comes: when I purchased the shield I was not aware that it can only supply 2A peak current.
However, my DC motor rating is 12v 5A. So I purchased a 12v 5A power supply.
But now I am not sure to operate shield with external power of 12v 5A.

Does it works or will it burn?
The shield will "burn". You need a shield that can provide minimum 5A per channel to run a 5A motor.

However, your motors aren't 5A. They have a stall current of 300mA, which is well within the capabilities of the motor shield, and the 5A power supply you have would barely even notice they were there.