It really depends on how busy the resort is. Getting there at 5am isn't going to help you if no one is checking out of the room type you want and there aren't any already vacant. The earlier you arrive and check in, the more possibilities there will be. The earliest I've ever been able to check in is around 5:30-6am (you have to wait until they change over from one day to the next, and it happens around that time). Once the changeover has occurred, the system knows which rooms are currently empty and which rooms are checking out that day. That will be the total pool of rooms available to people checking in. As people check in, the pool gets smaller.
If it's a slower time of year, I would say anywhere up to about 2pm you should have a pretty good choice of rooms. If the hotel is sold out, you have very little choice no matter what time you check in. Bottom line is, the earlier you CAN check in, the better your chances of getting what you want, but the busier the hotel, the less those chances are.