Almost there. You can't directly upgrade from 7.2.5 to 7.6.2 in a single step. Upgrades are limited and tested for only skipping 1 major release. The first 2 numbers of the AMP version constitute the major release. While the 3rd digit represents the patch release number. The reason for this limitation is changes to the database schema.
First, make sure the current existing hardware is still compatible. Compare the existing system with the AMP sizing guide posted on the support site. As you upgrade versions, you're getting additional features, some features require more disk space or memory resulting in the current sizing guide.
If the hardware is still good, then here's the main steps to plan out:
1. collect AMP backups to off server storage
2. AMP Upgrade Step 1 -> from 7.2.5 to 7.4.9
3. AMP Upgrade Step 2 -> from 7.4.9 to 7.6.2
4. OS Upgrade
Though you can do all 3 steps in a single day, I normally don't. I like to let the upgrade bake in to make sure that I've got a good backup between steps in case of any issues.
If you do choose to do all 3 in the same day, add steps:
2b. Take an AMP backup, pull it off server (this is a backup of AMP database in 7.4.9 format)
3b. Take an AMP backup, pull it off server (this is a backup of AMP database in 7.6.2 format)
The steps to upgrade the OS are outlined in this Airheads article: http://community.arubanetworks.com/t5/AirWave/AMP-7-7-will-discontinue-support-of-CentOS-5-RHEL-5/td-p/57254