There is nothing like reading the manual:
PHP: mysqli::select_db - Manual[
^]
You are using the procedural style of the method, and in that case the first parameter have to be the mysqli object to use and the second the name of the DB to select...
You have to options:
1. Fix the parameter order
$db_select = mysqli_select_db($this->conn, DB_NAME);
2. Use the OO approach
$db_select = $this->conn->select_db(DB_NAME);