MySQL on RDS Instance

I want to install WordPress on an existing AWS ec2 instance. However, I get an error: “Error establishing database connection”.

I followed the tutorial here.

The only difference is that the tutorial is for people who are installing MySQL on the same ec2 instance while I wish to have MySQL run on a separate instance (ie: RDS).

The steps I carried out:

1) Installed the httpd24, php56 and php56-mysqlnd packages on the ec2 instance.

2) Created a MySQL user with privileges and db:

CREATE USER 'wordpress-user'@'localhost' IDENTIFIED BY 'your_strong_password';
GRANT ALL PRIVILEGES ON wordpress_db.* TO "wordpress-user"@"localhost";

3) Filled out the wp-config values with the appropriate values:

define('DB_USER', 'wordpress-user'); //without the "@'localhost'" part
define('DB_HOST', '[RDS endpoint]:3306');

4) The rest of the instructions outlined in the tutorial (allow permalinks and file permissions for Apache web server).

However, when I enter the url of the WordPress blog I get the error: “Error establishing database connection”.

Does anyone have any suggestions for what’s wrong with my setup?

Thank you.