Ran into same problem. I just edited my /etc/php5/fpm/pool.d/www.conf file.
listen.owner = www-data
listen.group = www-data
listen.mode = 0660
2014/06/24 20:04:25 [crit] 2223#0: *10547 connect() to unix:/var/run/php5-fpm.sock failed (13: Permission denied) while connecting to upstream, client: <snip>
Update (Nice we can edit the posts now)
Looking into this more closely it looks like it fixes bug CVE-2014-0185 incorrect socket permissions.
The default PHP FPM socket permission has been changed from 0666
to 0660 to mitigate a security vulnerability (CVE-2014-0185) in PHP
FPM that allowed any local user to run a PHP code under the active
user of FPM process via crafted FastCGI client.
The default Debian setup now correctly sets the listen.owner and
listen.group to www-data:www-data in default php-fpm.conf. If you
have more FPM instances or a webserver not running under www-data
user you need to adjust the configuration of FPM pools in
/etc/php5/fpm/pool.d/ so the accessing process has rights to
access the socket.