While a category 4 deluxe family stateroom can certainly accommodate a family of 5 and you will have a verandah, it's usually not the most cost effective option.
On a cruise ship, prices go up as the cabin's square footage increases. The other factor is location. Staterooms on higher decks generally cost more. Category 4 staterooms are on deck 8.
Let's look at space:
Category 4 has 304 sq. ft.
Category 6 has 268 sq. ft.
Category 10 has 214 sq. ft.
Category 11 has 184 sq. ft. (no connecting rooms)
Category 11 staterooms are interior cabins. Staterooms can be adjoining (side by side) but there are no connecting rooms. Connecting staterooms have an interior door.
Families with older children might be fine with two category 11 staterooms. Another option is to book a Category 6 stateroom with a verandah and a Category 11 stateroom across the hall. This option usually prices out about the same as 1 category 4 stateroom. Many families with older kids enjoy this option. Parents get the luxury of a verandah and everyone gets more privacy!
Your most cost effective option is to price out two of the lowest category staterooms that fit your needs. If you need connecting staterooms, you would look at 2 cabins in category 10.
Finally, you want to look at
discounts. Since you are considering a cruise, go ahead and price out your options. Remember that you'll also save money by avoiding holidays.
I hope that you'll decide to discover the wonder and magic that can be found at sea!