STLRN,
There was actually a 3rd class of 5"/54, the Mark 16, that was originally designed as a lengthened barrel 5"/38 and was originally destined for the Montana-class battleships and was used on the Midway-class carriers.
In carrier use it was a single-mount gun, while the planned mounts for the Montanas were dual mounts.
It wasn't considered to be nearly as effecive, as it didn't have power ammo handling, and caused a lot of crew fatigue due to the large components.
Interestingly, the Mark 16 barrels were used on the later Mark 42 mountings, and the Mark 16 mounting was sold to Japan to arm its post-war destroyers.