I also think this is something you can accomplish if you really want to. I'm one of those annoying people that is always early and some of the things I do are set all my clocks 10 minutes fast as well as allowing 90 minutes every morning to do my chores, eat breakfast and hygiene before I need to dash out the door. Maybe you could even have a friend or DH call you to give you a prompting to get rolling?

I have a funky schedule and am very protective of my sleep also however if you are only 5 minutes late to work I don't really think it is about the sleep factor.