Your members table have EXACTLY 5 fields? If it have not exactly 5 fields you can not use the short form for INSERT.
In PHP variables, are you used in your SQL query is there any value?
Try to modify the end of your statement to see if MySQL will return an error:
$query10 = mysql_query("INSERT INTO members VALUES ('','$username','$enc_password','$name','Private')") or die("Error:" .mysql_error());