You'd probably get more response if you gave more info on your situation
and what you have already come up with as a tentative approach- how much
data in your 9.5 instance, what OS, what is acceptable downtime, etc.
Regardless, do you mean EDB Postgres Advanced Server or just one of the
installers that EBD provides for community Postgres?
If the paid software, then contacting EBD support would be your best
option. If using their installer for community Postgres, then I wonder why
and why not just use pg_upgrade which takes minutes.