In WHM you find at Home >> Service Configuration >> Configure PHP and suEXEC) to select a PHP handler
It is simple to upgrade and set php handlers if you are using EasyApache 3 or 4 version.
Finding
Software on the left menu and click on EasyApache 3
Select your Apache version, here I chose Apache 2.4.23
At step 2, you can select your PHP version as wanted, for example, i chose php 5.6.26
At this step, you should Exhautive Option List to explore Apache and PHP options in details
Click on any options to work for your website
Click on Save and Build
The building process will start for 5 seconds, if you don't want to wait, click here to start
After the process is complete, you should see this
Now you can enjoy new PHP version and options you set in WHM.
Hope that helped!