Personally, all those set-ups are only worth it if you know how to use every single one to their advantages, and the baits they were meant to chuck.
I personally don't even have that many technique specific rods. I have a bazillion rods, but I have multiples of the same kind from up-grading and such throughout the years. When I go fishing, I generally bring 2-4 rods with me on the boat. If I know I'll NEED 5 rods, I might bring more. The rods I bring to cover what I need are usually a Medium Light spinning rod for ned rigs, drop shot, tiny worms, a medium heavy as a do all (spinnerbaits, t rigs, lipless, etc), a heavy rod for bigger jigs and heavy carolina rigs, and then a second medium heavy with a different bait tied on just so I'm not retying my moving baits every time I feel I should throw a change-up in a certain spot.
My best advice, save all the money you would spend on 5 combos, and buy 1-2 really nice quality combos. And yeah, medium heavy is the go-to all around rod, and for good reason. One of my favorite rods is a 7'1 Medium Heavy and I throw everything on it. Frogs, jigs, t rigs, carolina rigs, you name it, that rod has caught fish with it. Is it the right rod for frogs and jigs? No, not by definition, but it catches fish and I've personally never had a problem with them tossing bigger baits upto 3/4oz.
The only time I really recommend technique specific rods are if you have cash to blow, are fishing extremely specific baits like a 3oz swimbait or a 2oz punching rig, or similar. Everything else can be covered by 1-2 rods.
Also, if you're bank fishing, that amount of rods becomes ridiculous. I tried carrying 5 rods around before and it sucks! 2 is my max if I'm hitting the banks, and it's always a spinning rod (medium light) and a medium heavy baitcaster.