Arduino and 5A 12Volt driver
I would wire up a Power N-FET, that could handle up to the full 5A and 12V across it, wire it in series between the LEDs' common-cathode and the GND, and pulse-width-modulate its base using the Arduino to control the brightness. That will give you the illusion of dimming, as brightness is a function of the average current experienced by the LED, and the physiology of the human eye will take care of the rest :).