Welcome aboard, Luigi87.
Yes, you can use a 5v power supply to run 12v LEDs. It is the best choice for your proposed setup.
1. The electrical difference between 12v and 5v LEDs is the current limiting resistor value.
2. The 12v LEDs won't draw as much current with the higher value resistor.
(Paradise Arcade 12v LEDs powered by 5v only draw 5.83 mA each vs ~20 mA powered by 12v)
3.. They won't be
quite as bright when powered by 5v, but they are still plenty bright IMHO.
(Wiring them in parallel won't reduce the brightness)
The big advantage to using 12v LEDs powered by 5v is the reduced current draw, especially if you ever plug into an un-powered USB hub. (USB spec is supposed to limit unpowered hubs to 100mA per port)
Just wire the LEDs in parallel like this using a 0.250" Quick-Disconnect daisy-chain.
If the LED doesn't light unplug/turn the LED 180 degrees.
Scott