$wordpress_user_db_query = mysql_query("INSERT INTO cedsite_wrdp1.wp_users (`user_login`, `user_pass`, `user_nicename`, `user_email`, `user_url`, `user_registered`, `user_activation_key`, `user_status`, `display_name`) VALUES
('".$username."', '".md5($pass)."', '".$username."', '".$email."', '', '".$date."', '', 0, '".$username."');");

Using PHP I am trying to do that, but it isn't working. Can someone help?

we need more information, how are you trying to use this? I see you are using Wordpress.

i.e. is it within a post? is it within a page? is it in a widget? is it in a custom template you are modifying on the backend? All would have different answers. I'll help if I can

try this

$wordpress_user_db_query = mysql_query("INSERT INTO cedsite_wrdp1.wp_users ( user_login , user_pass , user_nicename ,  user_email , user_url , user_registered , user_activation_key , user_status, display_name ) VALUES ('$username', 'md5($pass)', '$username', '$email', '', '$date', '', 0, '$username');");

Use only single quotes for inserting, not double quotes... this will give parser error... This will surely work fine