WordPress localhost multisite external view

I think I have to change the wp-config.php from ‘localhost’ to my new domain name? Whats the correct syntax? And if I do that it doesn’t seem to be able to access the database anymore.

I now signed up on a domain name and am pointing the A-record to my IP. when I type the url in a browser I can see the index page where I can see the subdirectory which wordpress is installed however when I click on that folder it resolves ‘localhost’ and obviously doesnt work.

my .htaccess file says this:
RewriteEngine On
RewriteBase /round5global/
RewriteRule ^index\.php$ – [L]

# add a trailing slash to /wp-admin
RewriteRule ^([_0-9a-zA-Z-]+/)?wp-admin$ $1wp-admin/ [R=301,L]

RewriteCond %{REQUEST_FILENAME} -f [OR]
RewriteCond %{REQUEST_FILENAME} -d
RewriteRule ^ – [L]
RewriteRule ^([_0-9a-zA-Z-]+/)?(wp-(content|admin|includes).*) $2 [L]
RewriteRule ^([_0-9a-zA-Z-]+/)?(.*\.php)$ $2 [L]
RewriteRule . index.php [L]

and my wp-config file says this:
/* Multisite */
define(‘WP_ALLOW_MULTISITE’, true);

define(‘MULTISITE’, true);
define(‘SUBDOMAIN_INSTALL’, false);

define(‘DOMAIN_CURRENT_SITE’, ‘localhost’);

define(‘PATH_CURRENT_SITE’, ‘/round5global/’);

define(‘SITE_ID_CURRENT_SITE’, 1);

define(‘BLOG_ID_CURRENT_SITE’, 1);