2 problems here:
one is as akdeja said , if there was a manned 5" gun then it is simply too easy to destroy aircraft like fighters.
Theres no need to even hit the aircraft as there is a huge area to aim for and with the proximity explosions you can hardly miss.
the second is the 190a8 'sturmi' (if im correct in thinking this is the aircraft you are refering to?) in AH isnt actually the sturmbock at all. What we have is a standard 190a8 with the option to add the sturmbock 30mm cannon loadout.
The sturmbock had armour of almost twice the thickness of the standard 190a8 including 30mm thick plexiglass on the sides of the cockpit and also 440lb more weight(with resulting performance loss).Extra armour around amunition boxes and an extra thick radiator ring armour.
If we had this on our 190 it would be much stronger/more durable but by no means able to withstand large calibre (40mm+)anti aircraft fire.There really isnt an aircraft that could even todays aircraft can be downed by 40mm.
I can understand the frustration but if it was any easier to kill the CV it would really be pointless to have in AH.
As we cant have a realistically sized carrier fleet , amounting to tens (if not hundreds in some cases!) of ships the only option open to HTC is to raise the durability of the ship and add a fierce AA defence.