Feeding microcontroller and linear actuators (motors) with the same power supply
First of all I would look to see if the two motors will actually run at the same time.
If not then the 10A power supply, is fine.
If they do run together, for how long? (you mention 25% duty cycle), power supplies usually have a over capability for a short period of time, and batteries will supply more current but at a slightly reduced voltage, so if going slightly slower isn't an issue then this would be fine.
Then there is the question of do they really use all 5Amps, I very much suspect not, unless you are fully loading the actuator(750N), they prob run at 2-3 amps at most.
Secondly
Circuit protection, fuses or thermal shutdown links for the motors is required, better still instant overcurrent protection for them set at 1.2x nominal current.
Do some worst case tests and measure the current, set the protection to 1.2 x this.
Remember if there is an issue the supply voltage will start to drop, its now that the micro will suffer if the voltage dips too much and you have no protection/sensing.

So suspect the power supply is more than ok.