Cat 1 - 3 are considered concierge level suites and are priced as such. But they will all accomodate a family of 5.
Cat 4 is considered a family cabin. It's not concierge, so is less expensive, but still pricey.
Those are your only options if you all want to be together in the same room.
But as others have mentioned, depending on what category you want, you can most likely get two cabins for less than it would cost for one Cat 4 cabin and definitely for less than it would cost for a Cat 1, 2, or 3.
If you want connecting cabins with a door between them take a look at:
Cat 10 - if you're OK with inside cabins
Cat 8 or 9 - if you want ocean view
Cat 7 - if you want a navigators verandah (open air, porthole size opening)
Cat 5 or 6 - if you want a full, open balcony
You have a few other options if you don't need the connecting door and just want cabins that are next door or across the hall from each other.