5.7.8: 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.7.8
[RFC3463] (Standards Track) from the The Internet Engineering Task Force (IETF) definition for codes that end with X.7.8:
This response to the AUTH command indicates that the authentication failed due to invalid or insufficient authentication credentials. In this case, the client SHOULD ask the user to supply new credentials (such as by presenting a password dialog box).