A: 

You need to add a section that tells Apache to use mod_fastcgi to execute your php5-fcgi script using FastCGI. Try adding this to your website.conf:

<Location "/php-fastcgi/php5-fcgi">
   Order Deny,Allow
   Deny from All
   Allow from env=REDIRECT_STATUS
   Options ExecCGI
   SetHandler fastcgi-script      
</Location>

The SetHandler fastcgi-script part tells Apache to use mod_fastcgi when executing your php5-fcgi script. The Allow from env=REDIRECT_STATUS prevents visitors from downloading your php5-fcgi script directly by accessing http://mydomain.com/php-fastcgi/php5-fcgi.

Also, I use

FastCgiWrapper On

instead of the suexec binary you listed in your example. My Apache is compiled with SuEXEC support and I use SuexecUserGroup as you do. My SuEXEC works with this configuration - might be worth trying.

And of course I'm sure you've already checked, but make sure you have:

LoadModule fastcgi_module modules/mod_fastcgi.so

somewhere in your Apache configuration.

blt04
Thank you for answer. I couldn't make it to work with fastcgi but I made it to work with fcgid.
Engrost