5.4.4: 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.X.X
[RFC3463] (Standards Track) from the The Internet Engineering Task Force (IETF) definition for codes that end with X.X.X:
The mail system was unable to determine the next hop for the message because the necessary routing information was unavailable from the directory server. This is useful for both permanent and persistent transient errors. A DNS lookup returning only an SOA (Start of Administration) record for a domain name is one example of the unable to route error.