def METHOD_NAME(cluster_name, db_name, admin_name, admin_password, rds_client):
    """
    Creates a serverless Amazon Aurora database cluster and a MySQL database
    within it.
    :param cluster_name: The name of the cluster to create.
    :param db_name: The name of the database to create.
    :param admin_name: The username of the database administrator.
    :param admin_password: The password of the database administrator.
    :param rds_client: The Boto3 Amazon RDS client.
    :return: The newly created cluster.
    """
    try:
        response = rds_client.METHOD_NAME(
            DatabaseName=db_name,
            DBClusterIdentifier=cluster_name,
            Engine='aurora-mysql',
            EngineMode='serverless',
            MasterUsername=admin_name,
            MasterUserPassword=admin_password,
            EnableHttpEndpoint=True
        )
        cluster = response['DBCluster']
        logger.info(
            "Created database %s in cluster %s.", cluster['DatabaseName'],
            cluster['DBClusterIdentifier'])
    except ClientError:
        logger.exception("Couldn't create database %s.", db_name)
        raise
    else:
        return cluster