I think the only stateroom that accomodates 5 people is Cat 4. And then there are the suites, Cat's 3, 2, and 1.
We are also a family of 5, so I feel your pain! Your best bet is to look at two connecting cabins -- there are a variety of these on the ship, although I can't say for sure if there are any inside connecting cabins. The nice part about two cabins is you get an extra bathroom, which can really come in handy. Be sure to book early, though, as these go fast.
On our last cruise, we had two connecting Cat 8's, and they suited us perfectly. The three kids slept in one room, and DH and I in the other. We had our privacy and a place to put our things without them being rifled through, etc. And they had their own place to keep their things, and of course their own bathroom. It really worked out great.
On our next cruise, in order to take advantage of a Kids Sail Free promotion, we had to book all of us in a Cat 4. The cost is reasonable, but I am not totally looking forward to us all being together in one room, as much as I love my wonderful family!