We are also on a 5 day double dip at CC next year. Compared to Alaska, you will be on a much bigger ship. That's twice as many people, though you likely won't know the difference except in a few things. I don't think they have an official formal night, though the
Disney Cruise site only addresses a 4 night cruise. However, normally on cruises less than 7 nights it is "optional dress up" and the term optional is key. You will have a range of shorts and sandals to tuxedos. Kind of weird to see, but works pretty well. Castaway Cay is an awesome experience and worth doing twice in a week. You can look at their activities or just enjoy a nice day at the beach. Nassau has mixed opinions and you can probably find a lot on these forums.