Unsure what you plan to do.
You can power an Arduino with a 12VDC supply. That works fine.
You can not power a 5V motor with a 12V supply, unless you keep it submerged in liquid nitrogen to deal with the heat.
You can not power a 5V motor directly off an Arduino, motors draw too much. The maximum a pin can supply is 20 mA; the maximum an Arduino can supply through its Vcc pin is a couple hundred mA so while small motors may work it's a bad idea - they draw a lot more than rated current when stalled and starting up.