by Ken Task.
First, no first hand knowledge if Softaculous upgrades works or not, but a few considerations before you click:
Have you ever restored from a fill site backup before? If not, review/study the process with your system.
Current version of your Moodle is 2.5.2 and assume the button would upgrade to 2.6.3. Upgrade and check out site for functionality/errors, etc. Then revisit the Softaculous upgrade to get site to 2.7 ... however ...
2.7 now has different requirements. According to download page: PHP 5.4.4, MySQL 5.5.31
Are those versions accessible to you? If they are, plan how to do those changes to your account before getting into 'la-la-land'.
Please do report back your experiences and do share where you host.
'spirit of sharing', Ken