In order to fix the php5-fpm.sock failed error follow these instructions

1) Make sure your virtual hosts nginx (.conf) files are using fastcgi_pass unix:/tmp/php5-fpm.sock; at the php-fpm configuration.

2) Edit nginx.conf file and make sure this variable is as follow:

user  nginx;

3) Edit /etc/php-fpm.d/www.conf file and set this variables as you see below:

listen = /tmp/php5-fpm.sock
listen.owner = nginx
listen.group = nginx

4) Reload your services:

service nginx reload
service php-fpm reload

All done, your websites now shouldn’t face any more 502 permission/owner issues because the socket has the same group as Nginx:

[root@node3.server.com:~]ls -ahl /tmp/php5-fpm.sock 
srw-rw---- 1 nginx nginx 0 May  6 08:08 /tmp/php5-fpm.sock

At this point, if you are still facing 502 Gateway timeout issues, check out this other post:

php5-fpm.sock failed (13: Permission denied) error