Help to redeem my purchase
i cant find quick links anywhere in the app store to redeem my purchase of OSX Mountain Lion
iMac, Mac OS X (10.5.8)
You can open the Mac App Store from the Apple menu. Go to Featured/Quick Links/Redeem
However, you're showing that you have OS X Leopard 10.5.8. There is no Mac App Store in Leopard. You need a minimum of OS X Snow Leopard 10.6.8 to have the final public release version of the Mac App Store. You need to buy Snow Leo on install DVD from the Apple telestore. Then use the update combo to bring it to 10.6.8.
OS X Upgrades -
A Mac that can run OS X 10.6 Snow Leopard can usually run OS X 10.7 Lion. And a Mac that can run OS X 10.8 Mt Lion can also run OS X 10.9 Mavericks. Lion, Mt Lion and Mavericks can all be installed over OS X Snow Leopard 10.6.8, so you may upgrade from Snow Leopard directly to any of the other three. Both Lion and Mt Lion are paid upgrades, while Mavericks is a free upgrade. You may also upgrade directly to Mavericks from either Lion or Mt Lion.
System requirements for OS X Snow Leopard & OS X Lion
http://support.apple.com/kb/ht4949
System requirements for OS X Mountain Lion
http://support.apple.com/kb/HT5444
System requirements for OS X Mavericks
http://support.apple.com/kb/ht5842
OS X Snow Leopard 10.6.8 v1.1 update combo