Using IUS (Inline with Upstream Stable)--a nifty repository provided by EPEL--we can upgrade beyond PHP 5.4 by first removing our current version of PHP, installing our preferred version (5.6 in our case), and then restarting Apache:

$ sudo yum remove php-cli mod_php php-common

$ sudo yum install mod_php56u php56u-cli php56u-mysqlnd

$ sudo apachectl restart

Sources:
https://www.digitalocean.com/community/tutorials/how-to-upgrade-to-php-7-on-centos-7
https://ius.io/GettingStarted/