Hello. You can disable open_basedir in your hosting control panel. Or set a rule:
open_basedir = Off;

in the php.ini file or this rule:

php_value open_basedir Off

in .htaccess file.

Write to the technical support of your hosting. The open_basedir control has nothing to do with WebSite X5.

I looked at manolatos.gr. It seems to me that you have not uploaded the site to the root folder of the site. Find out in the technical support of your hosting where exactly you need to upload the site.