I don't understand what you mean by the thickness depending on age, but I can tell you that ostriches do not live for five hundred years.

Egg shells are made of a biopolymer of protein filled in with a mineral substrate (I want to say calcium carbonate, but it could be phosphate). In order to dissolve the shell, you need something that will dissolve the mineral, which can happen in water or, especially, in any kind of acid. Left out without a liquid environment, the protein will eventually degrade as well even if the mineral does not, but losing the protein makes the shell brittle, not dissolve. So, if your egg shell has been sitting there undisturbed for five-hundred years in a dry environment, then it will still be there - but apply almost any kind of force to it, and it will crumble.