Attaching the adapter and the mirror is going to be a bit more complicated. The best way would be to bolt the mirror to the adapter and use studs to attach the adapter to the door after attaching the mirror. finding a way to accomplish this is going to be a bit tricky. I had thought, it might be easier to drill a hole for the wires through the adapter and attach them to the contacts then just glue the mirror to the adapter and glue the adapter to the door. This method, however, would make any replacement or repairs impossible. Perhaps Mr Bishop has some nifty ideas to accomplish the attachments.
This picture is the gasket of the OEM mirror and nicely shows the placement of the holes in the door.
This is the underside structure of the C5 mirror. Earlier I had removed part of this mounting thinking I could shape it to fit the door. It didn't work
This is a side view of the mount
The gasket shows the shape of the mount for the C5 mirror
Perhaps this is the most helpful. I did a rubbing of the C5 mirror then cut a hole and poked the mount through the graph paper
When I cast the Bondo between the door and the adapter, I was able to get a faint indication of where the hole is in the door for the OEM mirror
Here I try and show the alignment of the C5 with the adapter