Feeding microcontroller and linear actuators (motors) with the same power supply I have already made a diagram using a motor controller. I want to use only one power supply to feed arduino and motors. I want to use MDD10 dual motor driver.

The details of the actuators each one is:

Input voltage: 12VDC,
Max Load: 750N(168.607lbs),
Stroke Length: 16 inch,
Travel Speed: 12mm/s,
Duty Cyle: 25%,
Current: 5A.

The power supply is 12V, 10A.

Could you please check if it is ok, or which would be the best solution?

Some of my concerns are:

Be sure if the feed of 12 volts for the motors, and 5 volts for Arduino are correct and can live together as shown.

Be sure if the wiring for the Arduino, driver and motors is correct since it looks kind of simple.

I want to know if this is the natural approach by doing it with a voltage regulator to feed the Arduino and with 12V 10A power supply to feed the motors, or if there are other, better options to make the circuit feed only using one power supply (12V, 10A).

MDD10 Datasheet Link: https://www.robotshop.com/media/files/content/c/cyt/pdf/cytron-10a-7-30v-dual-channel-dc-motor-driver-shield-datasheet.pdf

Thanks in advance

UPDATE

I have increased power supply to 13A, also changed the linear voltage regulator (7805) to a switching voltage regulator (OKI-78SR-5), what do you think about this approach?

Or I should try with the 12V DC Vin of Arduino(I understand that it works with a linear voltage regulator)? Being this option, it could be maybe with a voltage pre-regulation stage(for example from 12V to 9V) or maybe connecting directly to the jack.

Thanks, Best Regards.
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.