Can I run php 5.6 in a specific directory?

I assume you used EE to set up the wordpress site. You just need a separate location block for the old site.

Here's an example.

This is the content of the file /etc/nginx/sites-available/mbt.192.168.0.210.xip.io

server {
    server_name mbt.192.168.0.210.xip.io   www.mbt.192.168.0.210.xip.io;
    access_log /var/log/nginx/mbt.192.168.0.210.xip.io.access.log rt_cache;
    error_log /var/log/nginx/mbt.192.168.0.210.xip.io.error.log;
    root /var/www/mbt.192.168.0.210.xip.io/htdocs;
    index index.php index.html index.htm;
    include common/php7.conf;
    include common/wpcommon-php7.conf;
    include common/locations-php7.conf;
    include /var/www/mbt.192.168.0.210.xip.io/conf/nginx/*.conf;
}


server {
    server_name test.192.168.0.210.xip.io   www.test.192.168.0.210.xip.io;
    access_log /var/log/nginx/test.192.168.0.210.xip.io.access.log rt_cache;
    error_log /var/log/nginx/test.192.168.0.210.xip.io.error.log;
    root /var/www/mbt.192.168.0.210.xip.io/htdocs/old;
    index index.php index.html index.htm;
    include common/php.conf;
    include common/locations.conf;
}

These three lines are the important ones.

server_name test.192.168.0.210.xip.io www.test.192.168.0.210.xip.io;
root /var/www/mbt.192.168.0.210.xip.io/htdocs/old
include common/php.conf;

Let me know if you need further help.