Our family of five is booked on a guar OV on Carnival Triumph in July. Five in one cabin! The cabin has two twins that convert to a King, a sofa bed and upper bunk or 2 upper bunks - cabin steward will bring a rollaway each night. There are limited number of rooms that accomodate five but these rooms do exist!
I have done some research on this factor in looking for a 7-day summer Caribbean Cruise that could accomodate our family of 5. This is what I found:
Carnival Cruise Lines have larger standard cabins than other cruise lines. Staterooms are available that can accomodate 5. According to my research these ships can accomodate 5 in a cabin by adding a rollaway bed: Fantasy Class Ships--Fantasy, Esctasy, Sensation, Fascination, Imagination, Inspiration, Elation and Paradise, Holiday Class Ships, and Destiny Class Ships such as the Triumph, Destiny and Victory.
Carnival ships that offer adjoining staterooms for families are offered on: Destiny, Triumph, Victory, Conquest, Glory, Valor, Liberty, Freedom, Spirit, Pride, Legend and Miracle.
Royal Caribbean has family staterooms that can accomodate 6 on these ships: Adventure, Brillance, Enchantment, Explorer, Freedom, Jewel, Liberty, Mariner, Navigator, Radiance, Rhapsody, Serenade, Vision and Voyager. Royal Family Suites are also available and they can accomodate 8.
Princess Cruise Lines also has family suites with a balcony that can accomodate up to 8. I think they only have 2 of these rooms on a ship and so would book out fast. The Star Princess, Caribbean Princess and Crown Princess offer these suites.
Disney Cruise Lines offers a category 4 deluxe stateroom with verandah that sleeps 4-5. These ships include the Disney Magic and Disney Wonder.
Another option is to get adjoining staterooms, however this option can be more expensive as higher rates apply for the 1st and 2nd person in each cabin, whereas you would get a cheaper rate for the 3rd, 4th and 5th passenger if you are all in the same cabin. However a Royal Suite on RCL can be more expensive than getting an adjoining stateroom.
If anyone else had a stateroom on any of these ships that accomodate 5 they could confirm how accurate my research is.
Good Luck in finding a cruise!