5.7.13: Official Definition
5.X.X
[RFC3463] (Standards Track) from the The Internet Engineering Task Force (IETF) definition for codes that start with 5.X.X:
A permanent failure is one which is not likely to be resolved by resending the message in the current form. Some change to the message or the destination must be made for successful delivery.
X.7.13
[RFC3463] (Standards Track) from the The Internet Engineering Task Force (IETF) definition for codes that end with X.7.13:
Sometimes a system administrator will have to disable a user's account (e.g., due to lack of payment, abuse, evidence of a break-in attempt, etc). this error code occurs after a successful authentication to a disabled account. This informs the client that the failure is permanent until the user contacts their system administrator to get the account re-enabled. It differs from a generic authentication failure where the client's best option is to present the passphrase entry dialog in case the user simply mistyped their passphrase.