You are a first timer? No problem.
YOu need to use an H-bridge to produce the current capable of driving the require current through a motor (as you have realized, a uC cannot provide the current high enough to drive a motor). An H-bridge's purpose is to be able to switch the direction that current flows through the load (so you can control motor direction). The uC can switch on and off the transistors to control the larger flow of motor-level current. You PWM these inputs (and therefore produce a PWM in the motor current) to control motor speed.
So, it doesn't matter if the uC PWM only goes from 0 to 5V. As long as this is enough to switch on and off the H-bridge transistors, you can use whatever power supply you want for the motor. Google H-bridges. As soon as you find a schematic, it should be fairly obvious which is the motor power supply and which is the logic supply.