S.J.
5-6 am happens to be the time the sun is coming up now. Maybe he's waking up then because that's when it's getting light in his room. Try darkening the windows (taping up garbage bags doesn't look good, but works well for this.)
Moving to a later bedtime in an attempt to get him to sleep later doesn't work for a lot of kids. Sometimes they're just "programmed" to get up at a certain time. Moving the bedtime later might just make for an overtired kid.
Good luck!