Even with using a 5V solenoid, you won't skip the MOSFET, becouse they draw quite a few current (they have current 'peaks' at start).
And you will need a more powerful 5 v power supply than the arduino regulator. As the motors run at 12v, a same voltage solenoid is preferred.
Depending on the solenoid, you could even use a transistor. Don't be afraid of using mosfets, just do some research before (There are plenty of schematics on the internet) and if you use an N-Chanel MOSFET, you can drive it without a transistor. (I used a P-Chanel MOSFET becouse it was what I happened to have around) Don´t forget the diode, or you will fry your MOSFET.
Also I found usefull adding a led, so I could see when the solenoid was activated.