If your ATX is already powering other things successfully on the 12V supply then there should be no issue using the 5V supply too. In fact you can typically take about 0.5-2A from the 5V "standby" power even when the main power from the ATX is turned off (check the specs of your particular supply).
You would just connect +5V (red wire) from the ATX to the 5V pin of your Arduino and Gnd of your Ardu' to Gnd of your ATX. Don't use the "Vin" because you need 6.5V or so on that pin to power the regulator. If you are using standby power then take it from the purple wire to 5V on your Ardu' instead.
Edit - But in any case, if you have a stable 12V that should be OK direct to Vin. If it's a little high, you can just run it through a few ordinary rectifier diodes first - 1N4001 etc can handle 1A of current and drop the voltage by about 0.8V each, so if you are reading 14V just put it through 3 diodes in series to burn off a little of that excess first.