Error: "the recipient has been rejected by the server, response from server 550 5.7.1 relaying denied"

Please check that you have activated the "my server requires authentication" option in your outgoing SMTP server settings.

You'll find this setting right at the bottom under the "servers" tab in this account's settings in Outlook Express, or in "Additional Settings" -> "outgoing server" in other Outlook versions.

The correct and complete settings for the various email clients can be found here.

After this delete/move the waiting to be sent messages (outbox) and try with a new message.