I wanted to put this out there to save the next person who runs into this will save time on researching it as I found nothing at all relating to this. I can successfully enabled Replication between two systems for some VMs but not for others and the error 80070005 was reported for them.
Long story short if you're getting "Replica server failed to authorized the connection" with error 80070005 and none of the other threads and posts sound like your issue check the VM IDs. If you've ever exported a VM from one machine to another and then imported it and told it to keep the same ID instead of creating a new one then that's the issue.
You wont find the answer on the machine initiating the replication but on the machine accepting it.
Event Logs -> Applications and Services Logs -> Microsoft -> Windows -> Hyper-V-VMMS
You should find Event ID 29284 errors that will give you the answer. Even though the VMs reside in different locations on the systems and have different names their VM IDs are identical. The machine your attempting to replicate to is denying the replication creation process because it does not believe you have the right to modify the VM it has with the exact same ID.
The only method of changing a VM ID I know of is to export and then import the VM having it create a new VM ID. After this has been done there is no longer a VM ID collision and you can enable replication.
Systems Administrator Senior - University of Central Florida