Newbie needs advice on simple project

webhansen:
doesn't the servo go at max speed if it's a 5V servo getting 5V?

It will try to, but the servo could easily draw more current than the Arduino's voltage regulator will provide. While you may be able to get it to move, as you've shown here, it will have limited torque and speed. Give it a separate reliable power supply to make sure it's working to its full potential before you look for problems elsewhere.