We just finished upgrading to Exchange 2013. When we use DB mail in SQL we are unable to send mail outside the domain unless we use an Exchange Admins account to send mail.
I have anonymous enabled on the Receive Connector on Exchange 2013.
system.Net.Mail.SmtpFailedRecipientException: Mailbox unavailable. The server response was: 5.7.1 Unable to relay is the message from SQL.