Carnival does allow five in some cabins.
Here is some info on Royal Caribbean family cabins ...
Royal family suite with balcony
Square footage: 533 to 586 sq ft
Balcony square footage: 139 to 193 sq ft
Occupancy: Up to 8 guests
Amenities: Private balcony; living area with double sofa bed; two bedrooms, each with two twin beds that convert to a queen-size bed; two bathrooms, one with whirlpool bathtub; vanity area; hair dryer; minibar; closed-circuit TV; radio; and telephone Cabin layout
and ...
Family oceanview cabin
Square footage: 319 sq ft
Occupancy: Up to 6 guests
Amenities: Picture window, sitting area with sofa and/or Pullman bed, two twin beds that convert to a queen-size bed, private bathroom with shower, vanity area, hair dryer, minibar, closed-circuit TV, radio, and telephone
And Disney is another option. Here is some info on the Disney Cabins ...
Deluxe family oceanview cabin with balcony
Square footage: 304 (including balcony)
Occupancy: Up to 4 guests (some sleep 5)
Amenities: Enclosed private balcony, one queen-size or two twin beds, ample closet space, privacy divider, single convertible sofa, Murphy bed, private split bathroom with bathtub and shower, hair dryer, cold box (refrigerator), TV, telephone with voicemail, individual climate control, and in-room safe.
