Default VestaCP instillation for CentOS 6.7 comes with PHP5.4 .
1. Install the REMI and EPEL RPM repositories
wget https://dl.fedoraproject.org/pub/epel/epel-release-latest-6.noarch.rpm && rpm -Uvh epel-release-latest-6.noarch.rpm wget http://rpms.famillecollet.com/enterprise/remi-release-6.rpm && rpm -Uvh remi-release-6*.rpm
2. Edit /etc/yum.repos.d/remi.repo
vi /etc/yum.repos.d/remi.repo
Under the section that looks like [remi] and [remi-php56] change:
from enabled=0 to enabled=1
Save remi.repo and exit
3. Upgrade PHP 5.3 to PHP 5.6
yum -y upgrade php*
See also: VestaCP Upgrade MYSQL 5.6