If you want to power all 12 at once, you might as well put them all in series and drive them from a current-limited power supply. 5 watts at 3.5V is 1.4 amps, so you will be running the total string at somewhere around 1.4 amps for full brightness, less current for less brightness.
3.5V * 12 LEDs is 42V, so you will need a power supply capable of 42V at 1.4 amps, with adjustable current limit. Unfortunately, that's not a common voltage. Surplus printer power supplies put out roughly 32V and laptop power supplies put out roughly 20V. But if you look around, you'll find something that will work.
As an alternative, you could connect them as two strings of 6 LEDs and power them from a surplus laptop power supply with series resistors for current limiting. I would try putting 2 ohms in series with each string of 6 LEDs. 2 ohms * 1.4 amps = 2.8V drop. If that's too dim, you might lower it to 1 ohm but don't go any lower.
42V is considered relatively safe, so as long as you are reasonably careful, you can wire this yourself. Anything above 48V is considered high voltage and needs special precautions.
Even though they are LEDs, they will still waste some energy, and that will be heat in the aluminum baseplate. The common solution is to attach them to a piece of aluminum which will dissipate the heat. If you don't do that, they will get very hot and fail.
