Just to be clear I used the new A7R V in a Nauticam NA-A1 housing for one project.
The LCD is thicker and longer than those from previous A7 line and A1 cameras. As a result with a housing where the LCD sits flat against the rear of the camera most housings will not close without the LCD pressing against against the LCD window and in many cases it will not close at all.
Nauticam housings have a deeper back plate that allows the LCD screen to be tilted about 20 degrees to give a better downward view of the LCD. If you remove the little stop on the rear of the tray (has a small screw) you can get the LCD on the rear of the A7R V to fit without pressing against the rear LCD window on the A1 housing. NOT ALL of the controls lineup and this would very for a Nauticam A7R IV housing. The controls that did work allowed me the turn the camera on and off, I was able to control Aperture, shutter speed and ISO. I could review images and the lower four way arrows mostly worked. I don't do video so not sure about those controls. If you don't remove the little stop from the tray the LCD could be damaged trying to close the housing.
I understand the A7R IV being able to fit into the NA-A7R V housing with a conversion kit but it is unlikely that it would work the other way around because the A7R IV housing will not be deep enough for the A7R V to fit. I suggest that if you have the IV housing and the V body that you try with the combination with the stop removed and see if any of the controls lineup and if the housing will close.