MQTT 5.0 will not be part of 3.12.x. It will be released in 3.13 earliest (possibly later).
User Property might come closest, however:
"The Server MUST send all User Properties unaltered in a PUBLISH packet when forwarding the Application Message to a Client [MQTT-3.3.2-17]."
Therefore, even though the MQTT 5.0 protocol is a bit more flexible with more headers, whether we can include a server set timestamp into the headers is up for discussion.
Strictly following the spec, we cannot include server set headers into the PUBLISH packet.
Note that User Properties in other packet types allow interpretation between Server and Client:
User Property in the CONNECT packet:
"User Properties on the CONNECT packet can be used to send connection related properties from the Client to the Server. The meaning of these properties is not defined by this specification."
User Property in the PUBACK packet:
"This property can be used to provide additional diagnostic or other information."
User Property in the SUBSCRIBE packet:
"User Properties on the SUBSCRIBE packet can be used to send subscription related properties from the Client to the Server. The meaning of these properties is not defined by this specification."