PHP 5.5 end of life is 10th July 2016.
Applications still using 5.5 should be upgraded to PHP 7 ideally or failing that 5.6 as a minimum.
Upgrading to 5.6 should be painless. Everything works without changes.
PHP 5.5 released in 2013, end was supported till 10th July 2015. Today security support has ended.
Any vulnerabilities that may exist in PHP 5.5 will NOT be patches any more and could leave your site vulnerable to attack.
If you host does not have 5.6 or higher you should leave your hosting company.
To test PHP version you can use