Upgrade Mac OS X from 10.8.5 to 10.10.5 How do I upgrade my Mac OS X from 10.8.5 to 10.10.5?

I obviously can't use a 10.9 or a 10.10 Combo Updater.
To upgrade from 10.8.5 to 10.9 or 10.10 you had to "purchase" Mavericks or Yosemite in the Apple App Store previously. Purchase is overstated because it was free then. After launching the final El Capitan 10.11.0 in the public the possibility to get the former systems in the store is gone if they don't populate your purchase list.

The Combo Updaters only update a system to a later or the latest point release:

10.9.1 -> 10.9.5 or
10.0.0 -> 10.10.5