Exponent CMS v2.0 was originally released supporting PHP version 5.2.1 or later, which at the time was v5.3.x. Support for PHP v5.4 was added in Exponent v2.0.7. Support for PHP v5.5 was added in Exponent v2.2.1. Support for PHP v5.6 was added in Exponent v2.3.1. Support for PHP version 5.2.x was DROPPED in Exponent v2.3.2 because several of the supporting libraries no longer supported such an old version of PHP. And support for PHP version 7.0, the current stable release was added in Exponent v2.3.7.
Most site administrators have little control over which version of PHP their web host server is running, but some hosts do offer a selection within their 'control panel' settings. Therefore, you have to trust your web host provider in keeping your PHP versions up to date since many of the updates remove security vulnerabilities. PHP version 5.2.x has been obsolete for quite some time. PHP version 5.3.x was termed 'end of life' meaning it was no longer updated in August 2014. PHP version 5.4.x was termed 'end of life' September 2015 and PHP version 5.5 reached 'end of life' a few months ago. With that being said, PHP versions 5.6.x and v7.0.x are the only recommended and supported versions available, both of which will be supported until at least late 2018. PHP version 7.1.x should be released before the end of 2016 and is in beta testing now.
Therefore, if you have a new enough version of Exponent to support a newer version of PHP, you should probably encourage your web host provider to move to it to prevent security attacks from harming your site or data. Furthermore, running PHP v7.0.x will give your site a tremendous speed increase because it is so much more efficient. The next version of Exponent (v2.3.9) will be released in a few days and supports PHP versions 5.3.x, 5.4.x, 5.5.x, 5.6.x, and 7.0.x and likely supports 7.1.x though testing isn't complete. You can expect Exponent to drop support for PHP v5.3.x very soon, with v5.4.x support not being provided too much longer either.
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Exponent CMS Developer