Since Royal Palm is basically a timeshare most available rentals will be by the week with either a Sat., Fri. or Sun. beginning and in that order. To rent from an owner you would have to rent back to back weeks. I would suggest checking HERE. I did a quick check and found availability for around $215/night. There are taxes and resort fees involved that bring the total daily rate to around $270/night.

It is going to be tough to rent 5 days any other way. You might also try some of the travel sites.