You can receive emails just fine but sending emails gives you a "550 5.1.1 User Unknown" error. When this happens, delete all pending email in your outbox. Try sending again. That should fix it.
If you Googled "550 5.1.1 User Unknown" you'd get a lot of results pointing to a problem with Exchange server settings. The average end user isn't likely to have an Exchange mail server so more likely it's the email the mail client software is trying to send that's the cause of the problem.