Waking up early has absolutely no bearing on success.
I've been working for myself for going on 4 years now, and I get up every day at about noon after working till 5 or 6am.
Waking up early = success is a huge lie that has been perpetuated for decades by companies like IBM.
I used to feel like a loser every day when I woke up at noon but then I started realizing: "I made $4,000 while I was sleeping, I can wake up whenever I damn well please."
What people don't realize is even though I sleep till noon I still sleep WAY less than the average American.
Do you have a family? Kids? Employees? Wife (who works a 9-5)? An office?
The wake early thing will have no bearing on you what-so-ever if you don't have other commitments to juggle work around, which I'm guessing is true if you're living on a schedule of midday -> 5am.
If you work with other people, and have an office, or kids you want to see after school and spend time with, sick grandparents you have to look after, etc then waking up early is best way you can get in a couple hours of truly productive "on your own" work time, without interruptions or feeling guilty for neglecting another commitment.
I tended to perform best on a schedule similar to yours, as a pretty typical night owl, but now I have an office and have to work with other people during the day, plus set a "good example" by being in the office consistently, and on time. That means I need to be in the office for the entirety of the 9-5 window. To get in productive "alone" time I'd either have to stay in the office very late (until 2am, before going home) or leave the office, then come back at midnight or something stupid, or just get up a couple hours earlier and get in for 7/8am. Ended up going with the latter, and it's working well.
Any time from 5pm -> 2am can easily end up rescheduled. Social things get in the way, people asking you to do things, and so on.
5am -> 9am never gets rescheduled.