We have struggled with this at times with our 6 year old.

When he started a new school this fall, he was up about 4:30 for awhile, and up before 6 for months. It really stank.

His behavior deteriorates markedly when he is tired, and he WAS tired. We tried all kinds of things to deal with it, and we were SO relieved when it finally ended. :p We tried putting him to bed a bit earlier. We talked to him endlessly about it and how important it was to sleep later. We forbade him from TV and GameBoy and anything else we thought might be getting him excited to be up early until after 7. (These things aren't allowed much anyway, but briefly we had allowed GameBoy when he was up too early and we regretted it.) We pointed out all sorts of things we couldn't do with him in the evenings because we had to put him to bed so early without fail every day. We tried to talk to him about relaxation things to try to go back to sleep, etc.
But it felt like it went on forever...
I do think he was a bit anxious starting new school. Not depressed. For our son the issue is behavior, but I certainly could imagine it affecting learning instead.
Just last week he had a cough that woke him at 4:30, and he hasn't ever in his life been able to go back to sleep once he is truly up after that time so he was up. :rolleyes: This happened one more day and the next time I gave him a narcotic cough syrup at 3:30 when he had a coughing fit and since then he is back getting up near 7. Whew!!
Good luck!!!