Recommend the following site:
http://www.navweaps.com/Weapons/WNUS_5-25_mk10.htm
Figure the ROF is high as listed- (fixed charges -vs- separate ). The smaller 4" and 3" guns were fixed ammunition. Trade weight in shot for velocity between the calibers.
Proj weight for 4" gun: 63lbs total, for 5" gun: 80lbs...
Surface action took alot of balls on a submarine. The afforementioned ammo chain, prep the gun from submerged tie down, and just being plain exposed.... hats off to those crews. Back in the day when I was in armor- our 105mm could pop a round every three seconds. That was with a ready rack right behind you, and the loader working flat out.
On a sub the rounds are flying slower (APFSDS was around 5,200+ ft/sec on the tank; 5"-25 listed on the given website 2,155ft/sec) and they'd likely want to observe each round. At roughly five seconds or so to 4,000 yrds.... yeah, ROF would be less. Of course, if that Jap destroyer caught you w/o being able to dive.... that ROF might just be amazing.