Use an ELV dimmer to dim an electronic switching power supply for LEDs

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 :).

Yes, LED strips have resistors built in.

Resistors are primarily rated by ohms (Ω), and secondarily by power dissipation. Standard component resistors are rated at 1/4W dissipation. That just means that you can't put more power through them without burning them out.

To figure out what to put in the resistor block of your circuit we'll just use Ohm's law (V = I R):

1. You should measure with an ammeter to be sure, but 5050 LED strips are typically assembled with resistors to draw 1 amp per meter at 12V, which means that the strips have built-in resistance of 12Ω.
2. Decide how much "dimming" you want. If you want them at quarter brightness, and noting that luminosity is proportional to current, then quadruple the resistance by adding a 36Ω resistor, which will bring total resistance to 48Ω and reduce current to .25A/m.
3. But you can't just pop any 36Ω resistor in front of the load. Suppose you have 1 meter of strips on your helmet: That would mean that you have to dissipate .25A*12V ≈ 3W of power. Therefore, either find a ≥ 36 Ω 3W resistor, or else use twelve standard 3 Ω 1/4W resistors in series, or twelve standard 432 Ω 1/4W resistors in parallel, in order to dissipate the power used by a meter of those LEDs.