Did you set up nginx to pass php files to php5-fpm? There should be something like this in your nginx virtualhost’s config:

        location ~ \.php$ {
                try_files $uri =404;
                fastcgi_pass unix:/var/run/php5-fpm.sock;
                fastcgi_index index.php;
                fastcgi_param SCRIPT_FILENAME $document_root$fastcgi_script_name;
                include fastcgi_params;

        }

If not, install php5-fpm and add the location {} block inside the server {} block and restart Nginx.

sudo apt-get install php5-fpm