Tag your bags.....sure, the DME luggage service doesn't officially start until 5am, but in all actuality? A flight landing at 4:59am, isn't going to be at the gate until close to 5:10. DME luggage people will be there.
When you get to your resort, your room may very well be ready. If you do on-line check-in and tell them what time you're arriving, you could get lucky. Whether or not it's ready, go get breakfast and then head to a park.