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What is the outgoing mail server you are sending from? Is it mail.bigpond.com or mail.otherdomain.com? Are you sending from your Bigpond service?
If it's not mail.bigpond.com and your using your Bigpond service to send the email, try opening up the email options and changing the setting something like, "My server requires authentication" to a tick and enter the username/password again.
The error is generated by the hosting mail server. So it's not likely to be Bigpond's fault.
For all my outgoing email sent from home (Outlook) regardless of the actual domain goes out via mail.bigpond.com
That way I have no issues sending and the return address is still the correct domain.