Install packages from Webtatic.

sudo rpm -Uvh https://mirror.webtatic.com/yum/el6/latest.rpm

Install Nginx 1.8

sudo yum install nginx18
sudo service nginx start

Install PHP5.6

sudo yum install php56w-common php56w-fpm php56w-cli php56w-mbstring php56w-gd php56w-mcrypt php56w-pdo php56w-mysql php56w-xml php56w-xmlrpc php56w-pear php56w-pecl-imagick php56w-pecl-apcu

Change cgi.fix_pathinfo=1 to cgi.fix_pathinfo=0

sudo vi /etc/php.ini

Update

sudo vi /etc/php-fpm.d/www.conf

Replace the apache in the user and group with nginx

[...]
; Unix user/group of processes
; Note: The user is mandatory. If the group is not set, the default user's group
;	will be used.
; RPM: apache Choosed to be able to access some dir as httpd
user = nginx
; RPM: Keep a group allowed to write in log dir.
group = nginx
[...]

Start up php-fpm

sudo service php-fpm restart

Install MySql5.5

sudo yum install mysql-libs yum-plugin-replace
sudo yum replace mysql-libs –replace-with mysql55w-libs
sudo yum install mysql55w-server
sudo service mysqld start
sudo /usr/bin/mysql_secure_installation

Setup auto start

sudo chkconfig --levels 235 mysqld on
sudo chkconfig --levels 235 nginx on
sudo chkconfig --levels 235 php-fpm on

*References:

Webtatic Nginx

Webtatic PHP5.6