If I recall, Carl tends to just use whatever lines came spooled on the random glass combos he gets off ebay, which occasionally includes sink tips of unknown weights). A lot of people prefer sinking lines (or tips) slightly heavier than the stated rod weight, and others may not.
5 and 6 are so close I doubt you'll notice any problems whatsoever, and it will save you some cash!
This year for shad I took a 250 grain sinking line with a 30' head, and cut off about 3' to make it more manageable for a fenwick ff706 (7-foot, 6-weight fiberglass rod). The 250 gr was fine, but I like a tiny bit less on that rod. Beth was using a fenwick ff80, which was (in this instance) a 8-foot, 7/8 weight rod paired with a 300 gr sinking line with about 4' of the head cut off. It worked extremely well.
This is mostly a lot of nonsense meant to inspire you to "try just about any darn thing" and it will probably work. They are all just stupid, thoroughly pointless "fish poles" in the end ;)
Gene