Although I do my best to accommodate everyone, I have had to make the stance only to support PHP 5.5+. If you run a site with a PHP version older than this I highly recommend you upgrade to at least PHP 5.6. Older versions of PHP are no longer supported and may contain security issues.
How to determine your version of PHP
This is a handy plugin that will display your PHP version on WordPress Admin dashboard:
PHP Development Team’s view
Previous versions to PHP 5.6 are no longer supported by the developers of PHP. As version 5.5 is still widely used I’ve decided it makes sense to support it.
WordPress’s view
As stated on WordPress.org’s requirements page, WordPress recommend that WordPress is run on a server that supports PHP 7+. They also state the following:
Note: If you are in a legacy environment where you only have older PHP or MySQL versions, WordPress also works with PHP 5.2.4+ and MySQL 5.0+, but these versions have reached official End Of Life and as such may expose your site to security vulnerabilities.