Hello!
Any success on upgrading from 2.5 to 2.8 now?
Remember there are three things you need to back up:
(1) The database.
(2) The moodledata folder which is NOT a publicly accessible folder, but hides away on your server somewhere.
(3) The moodle folder which IS publicly accessible from the web. This is the one that you replace with new version
After you have backed all three of these things up, you can rename the publicly web accessible moodle folder to moodleOLD then extract the new version which will create a new moodle folder in the same place with the new files. You then copy over the config.php from moodleOLD folder to moodle folder and upgrade should start the next time you go to moodle/admin/