Try the below settings and instructions and check if mails will go out. The below is how you should set up your mail when getting any authentication errors.
The correct SMTP settings to use with Outlook are
Outgoing Mail (SMTP) Server:
mail.domainname.co.za / servername.co.za
Use Authentication: Yes
Port for TLS/STARTTLS: 587
Port for SSL: 465
Server timeouts Greater than 1 minute, we recommend 5
DO NOT check the box for Secure Password Authentication. If your client does not support SMTP authentication, you won't be able to send mail through your client using the server name. If you're having trouble sending mail but you've confirmed that encryption is active for SMTP in your mail client, try to configure your SMTP server on a different port (465 or 587).