I think before you can decide if this means that you want to change jobs or careers - you need to get more sleep.

If you are waking up exhausted (and 5:15am is pretty early) your judgement is going to be clouded by how tired you are. Try going to bed much much earlier so you are more well rested then see how you feel after a week or so. If you wake up feeling refreshed and well rested yet still hate the idea of going to work...well, you might have your answer.

But until you can rule that out, don't make any hasty decisions. I can tell you that if I don't get a good night's sleep, I definitely wake up feeling like going to work sucks.