Upgrading PHP version should be under Software section 'Select PHP version' in Cpanel. If you don't see 5.5 then your plan doesn't include it.
Doesn't seem like it's possible.
I'm following the godaddy instructions and they are either incomplete or the possibility just doesn't exist for linux servers
I'm pretty sure a GoDaddy devops or someother tech has to do this... and they very much SHOULD. There's no excuse for PHP5.3 to still be lurking around.
chatted with someone yesterday. You need to purchase new control panel hosting to get newer PHP versions. They are perfectly happy to have us all use PHP that is no longer supported. Time for a class action.
Welcome to the Community!
How you upgrade the PHP and MySQL depends on the hosting plan you have in the GoDaddy account. For a MySQL upgrade on cPanel plans, you will need to contact customer support.
View or change your PHP version in Web & Classic hosting
View or change your PHP version in cPanel hosting
Upgrading a MySQL or MSSQL Database in Web & Classic Hosting