That's actually two questions, about shells and propellant/powder and the answers are "probably not" and "definitely not."

For this to make sense you have to understand how the ammunition for these guns works: The shells are separate from the propellant and often shared between different guns of the same bore. There were different types, like high explosive ones used for shore bombardments and armor piercing ones used for ship-to-ship combat. Stored in the ship ready to be fired, it looks like a man-sized bullet. Imagine a rifle bullet, removed from the cartridge, 14 inches in diameter and 4+ feet tall. The "gunpowder" (actually chunks of nitrocellulose the size of a D cell battery) was packed in cylindrical bags about the size of a rolled up sleeping bag weighing about 100 pounds each.

It's also important to note what "Caliber" means in this context. It's often used to mean the bore of the gun, but in naval guns "caliber" refers to the length of the barrel in multiples of its bore. A 14 inch 45 caliber gun is 45 times as long as it is wide, 14 inches wide and 52.5 feet long. It's common for guns of similar bore but different calibers to share some or all projectiles, but the powder might be different. I'm more familiar with the 16 inch guns of the later fast battleships, and the North Carolina and South Dakota classes used the same exact projectiles as the Iowa class, but the Iowas had longer barrels that required slightly different powder.

The 14 inch guns on the Texas entered service prior to WWI and were retired immediately after WWII with no plan on reactivating them. They used up some of the ammunition in training, some of the shells were dumped into the ocean, some were scrapped, some were deactivated and sold as memorabilia. I'm sure the Texas has quite a few of them on display, USS North Carolina has at least one full shell deck of 16 inch projectiles.

Now the powder: At the end of WWII, the Navy had a large number of 16 inch projectiles that the 4 Iowas could use, but not enough suitable powder bags. So instead of manufacturing new, they opened, examined and re-mixed powder from the 14 inch and earlier 16 inch guns to make more 16 inch 50 caliber powder bags for the Iowa class. And that's all of the battleship ammo that has ever been used since WWII. None has ever been manufactured after 1945. The shells fired during the Persian Gulf war in the early 90's were made during the Roosevelt administration.

The four Iowas took part in Korea, Vietnam, Various Cold War Shit and the Persian Gulf War, and even after all that, four decades of using WWII surplus ammo, the navy still had upwards of 15,000 16 inch shells and the powder to fire them left in inventory.

1940's America be BUILDIN shit.

As the powder aged, it became more unstable, so most or all of it has been destroyed by now and none new has been made since the invention of color TV. The stockpile of shells has either been scrapped or deactivated and sold for display; visit one of America's ten battleship museums, they've all got enough to make you sick of looking at them. We'll probably never hear those guns fire again, and here's hoping we'll never need to build more.

I'm less sure about the 5 inch guns, though I think the 5 inch guns in use today are a different, incompatible system than the WWII era ones.