You'd have to try & contact the Apple Store and sales support to see what happened
to the purchase of Mountain Lion 10.8, and where the confirmation email to you with
the download code for the App Store went to. And how to use it, once found, to get a
download from the App Store. You don't just buy the download from the App Store.
Here is the page where you'd start an order to purchase that operating system:
•OS X 10.8 Mountain Lion 10.8 Apple Store (US)
http://store.apple.com/us/product/D6377Z/A/os-x-mountain-lion
http://www.apple.com/contact/
Once the Mountain Lion 10.8 system is installed, you could run software update
or use the App store in it, to get this Combo OS X 10.8.5 Update, or use this link;
it will only download the Combo Update, this is not a full system:
OS X Mountain Lion Update v10.8.5 (Combo)
If you are in the US, or most countries, the 800 number in the Apple Store online or
in the Contact link in the bottom right of the main page, should direct you further.
Usually you can use the main number and ask for an OS X system specialist if you
have a question about the system, or how to go about purchase, or to confirm the
process you may be required to take to get and use a different system.
You may have to tell the person you talk to, the serial number, model number and
other relevant information in order to follow up on your previous activity there.
Good luck & happy computing! 🙂