Two things to note. I think it was Charles Poliquin who made the point that we are able to give the greatest amount of strength output three and ten hours after waking. This means that you will most likely perform somewhat sub par if you train immediately after waking. That being said I have spent years training at 5:00, 4:30, 5:30... and I find that the three biggest things are A) Hydration B) Food C)15-25 min.
Get up. Eat a banana and some yougurt. Drink a bunch of water. Keep moving around. Then hit the exercise... see how that goes. Just make sure to eat your recovery meals... and get some carbs in you. The body needs them at that point.