If an Iowa-class battleship materialized out of thin air within 5 miles of the center of a carrier strike group roughly, how much damage could it inflict before it was disabled or sunk?
Let's assume you mean a Japanese WWII Carrier strike group, say circa 1943.
At this time Japan only had 2 major aircraft carriers left. The Shokaku and Zuikaku.
The Tihou was not completed yet and the Shinano was still in the process of being converted into a Carrier. The rest of Japan's carrier force was made up of smaller light carriers like the Ryujo (through the Ryujo been sunk the previous yer, but you get my point).
Anyway Japanese Carrier doctrine was different than the Americans in several major ways. One of which was carrier groups fought as an entire air-wing rather than the more flexible air squadrons. It was this doctrine that helped lead to the major defeat for the Japanese at Midway. I know it sounds like I'm getting off topic here, but trust me it will help play into the theoretical battle you've asked for later on.
I can't find the diagram of what I'm about to explain next so just try and follow me. In order to launch their planes as an air-wing, two carriers would line up next to each other (plenty of space apart of course). They would then start launching their planes in opposite holding patters. One carrier's planes would go to port, the other would go to Starboard. Once all planes were aloft they would then go on their designated mission. The problem is this took a lot of time and if they had to do this while under attack it made it nearly impossible and made the carriers sittings ducks. This is unlike their American counterparts which, when a threat was detected, they would start launching immediately any plane that was ready or not. Along with their CAP (Combat air patrol) that was already flying. Now the Japanese weren't stupid and they would have CAP flying, but more often than not this wasn't enough and more planes were needed. This was hard to pull off with such inflexible launching procedures to follow. So any Battleship suddenly appearing would take a while for any response from the carriers to become a true threat. And their CAP were mainly fighters armed with bullets and not bombs. And by 1943 most of the carrier forces best pilots had been depleted. This left novices and poorly trained crews. So it would've taken even longer to react.
Now onto what ships would be protecting the Japanese carriers. Early in the war the Americans adopted the defensive screen or rings. On the outer ring would be the destroyers. The next ring would be the light cruisers. The next ring the Heavy cruisers. The next Ring the battleships, and in the very center were the Carriers. This defensive strategy was very effective. However the Japanese use the squadron based formations. Basically each carrier was assigned their own defensive squadron. These may or may not have been made up of 1 battleship, 2-4 cruisers, and roughly 8-10 destroyers. And their formations, instead of being circular, were diamond shaped. While this strategy allowed for some flexibility to the dwindling amount of Ships the Japanese could use, it was a poor defense in the long run. At this time the Japanese were still relaying on the "Kantai Kessen" or the decisive battle that would quickly end the war. Having formations in diamond formations would allow for a quicker and more effective response to close quarters range battle. But by now the aircraft carrier had become the ruler of the seas.
There was also a disparaging difference in technology coming out at this time. America's newest ships were being equipped with range finding radar. The Iowas were no different. While many Japanese ships had radar they were more passive and were mainly only used to alert them to a threat. Meanwhile American radar could determine range and altitude and even speed and direction of said thread. This allowed for far grater accuracy against both air and sea threats. They also had gyroscopes to help keep guns steady on target. Many of Japanese battleships and cruisers lacked both of these and mainly depended on optical range finders. These lost a lot of accuracy the further out a target was. Though since this battle will be at roughly 5 miles they will be somewhat accurate, but still not as accurate as range finding radar. American gunnery crews at this time were also getting better and better while the Japanese crews were losing more veterans everyday.
