Category 5 and Category 6 staterooms are identical -- except that Category 5 costs more. The only difference is that Category 5 staterooms are on deck 7, which is one level higher than the majority of Category 6 staterooms. I think deck 6 is actually a more convenient location, given that we made a lot more trips downstairs (to restaurants, shows, lounges, movies, shops, kid's clubs, guest services, and scheduled events) than upstairs (to the pools, deck events, and Topsiders).
In addition to considering different dates, another way to reduce the price is to consider less expensive room categories. A private verandah is a nice luxury, but the promenade deck chairs on level 4 are really a much better place to spend time and read. I will seriously consider a less expensive category (or perhaps two staterooms across the hall from each other for the four of us) instead of a Category 5 or 6 room next time.