Most of the rooms have a max of 5 so you should be fine. Check when you make your reservation (you have to register the names of all guests, at least when you book by phone, no matter the age) just to be sure.
They allow 5 in a standard room. We were going to have grandma come with us and they told us if there is more than 5 people then we need to get a 1 or 2 bd room suite. They said it was because of the fire code.
I would book it anyway. We booked DLH directly through Disney and there are 5 of us.
Also - that seems to be a great rate.
FWIW: All Disney hotels at WDW sleep 5 as long as the 5th person is under 3. (All Disney hotels at DLR allow our family of 5 to book a room.) At WDW it's only when the 5th person is 3 or over when you technically need to make sure the room truly accomodates 5. But even then, many people have the 5th person sleep on the floor.
Well I'm not sure about The Paradise Pier (think I read that's where you are staying), and I understand safety hazard and fire code, but over at the Disneyland Hotel they wouldn't notice how many people are in a room. You rarely run into any staff, just be respectful and don't make too much of a mess and the staff should not complain or suspect that there are too many people, unless the room is small. The DL hotel rooms can easily accommodate 5 adults, and a playpen.