Naval rifles (what landlubbers refer to as "cannons") are traditionally designated by the diameter of their bores and by caliber. But in this instance, the "caliber" designation is nothing like civilian firearms.
Caliber, for a civilian (or Army) firearm, has some passing resemblance to the bore diameter. It varies, usually for marketing reasons. A .357 magnum can trace its bore diameter back through the .38 Special, the .38 Long, the .38 Short and all the way back to the .36 of the Colt Paterson revolver. A .30 rifle has a bore diameter of .308", a .303 has a bore diameter of .311". A 7.62mm rifle can have a bore diameter of .308" (NATO) 0r .311" (Russian). A .44 is really a .43 (.429"). And so on.
Caliber, for naval rifles, is the length of the bore from the breech to the muzzle divided by the diameter of the bore. The main guns of an Iowa-class battleship had a caliber of fifty, which meant that the length of the gun barrel itself was 800 inches (16"x 50); the designation of a 16" gun was a "16'/50". A common small-caliber gun in use up until the 1970s was a 3"50, which meant that the gun barrel was 150" long.
The 3" round was the largest one-piece round (known as "fixed ammunition"), in that the projectile was mated to the cartridge case. The 5" has a separate projectile, the cartridge case contains only the powder ("semi-fixed ammunition"). The old 8" and 16" guns used bagged powder, a method of powder handling that dated back to at least the 18th Century. The last versions of the 8" guns used powder in cartridges. So did the light-weight 8" gun project of the the 1970s, which was canceled thirty years ago.
The predominant medium caliber gun through World War II was the 5"/38. (When the projectiles were fitted with one of the technological wonders of the war, the VT fuse, the 5" guns wiped out most of the Kamikaze attacks. ) The ships built from the 1950s on were fitted with guns that had longer barrels: 5"/54s. The 5"/54 Mk.42 had provisions for local aiming with positions for one or two gunners. The Spruance-class destroyers were the first to be equipped with the Mk.45 5"/54, which eliminated the gunner's position. A new version of the Mk.45 that sports a 5"/62 gun is supposedly in use, which has higher chamber pressures and would have been able to throw a new rocket-assisted projectile (RAP) out to 60 miles.
When I first heard about this project, I was dubious. The Navy experimented with 5" RAP back in the late `60s and early `70s. RAP was renown for having two problems. One was at the extended range, you couldn't hit a damn thing with it. Second was when you added in the rocket parts, you were left with a something which was not a hell of a lot more powerful than a hand grenade, which made the RAP the world's most expensive grenade launcher.
So, to get around those problems, the idea became to basically throw a GPS-guided rocket out of a 5" gun. The projectile was going to be a lot longer and heavier than a standard 5" rounds, which of course meant that it would take up more space in the magazine and it would be much slower to load. Because the projectile being thrown out was a lot heavier than a standard round, the cartridge cases contained more powder. As any rifle wildcatter knows, more powder means higher chamber pressures and shorter bore life.
Apparently, it didn't work very well and the project has been recently shitcanned.