This is our plan. As it currently stands, when we go in April, we have 5 day park hopper and on the last day (Dapper Day!) we will be upgrading to Flex AP with the plans to come again in November (extra nice after a 12 year break from the park!)
DH just realized that our flight doesn't leave until the evening of the next day, so we will be spending the departure morning at the park with our brand, shiny new Flex passes, since that is a "good to go" day.
As for "needing" a 6th day...
Growing up and as a teenager and early-20s-something, we always came down with the 5 day park hoppers. One of our last trips (before they did away with the 6 days) we added a 6th day, and that was fabulous.
No one probably NEEDS 6 days. Heck, no one really needs 5 days, probably. Most people can do almost everything in the park in a couple days. But we really enjoyed having that time to wander through, catch some shows, reride favourites... More Disney is better than not more Disney!
That being said, adding on Universal or Knotts or something else in the area is also a great option, as others have said, and for the money, probably more "bang for your buck".