Hi C.,
Your son has my sympathies...I had a job which required me to wake at five, and I quit when I was pregnant. I was so tired in the morning I wanted to cry, but was too tired.
So, you have a few options. First, put him to bed earlier. 5:30 is extrememly early for a kid to wake. A 7 o'clock bedtime would suit the situation.
Second, think about how you can make this transition easier for him, because asking a kid to be up and functioning at such an early time isn't fair to anyone involved. In regard to getting dressed, I'd find out if he could just go to the sitters in his pj's. He can pack a backpack of clothes the night before and change when he's more awake; you can pick up the backpack of pajamas the next morning when you drop him off. (I know, two backpacks--but it's easier than what you're doing right now, maybe!) Or see if he's be up for wearing his next-day clothes to bed. This is unconventional, surely, but will lessen the frustration of having to dress every morning. It's important to remember, too, that having to make decisions about which clothes to wear and having to get dressed is akin to waking up to a forced march each morning.
Between the change in sitters and the change in wake-up times, this is a lot for a young child. Nobody's fault...these things just need to happen. For what it's worth, as a nanny I've been privy to several different families mornings, and even at 8 or 9, kids are still needing a lot of support from parents to get out the door. Streamlining by picking out clothes the night before, etc. can help, but some kids are just tired when they wake, period. So, again, I'd urge you to try an earlier bedtime. Oh...and if it helps, my suggestion would be to also wake him up 15 minutes earlier. This might sound like hell, but it will give you a bit of a time buffer which could take the edge off a little.
My best to you and I hope something here helps or gives you an idea that will work for your family.