I'm using a GH4 for video in an Ikelite housing. Not being as compact as the alloy housings makes the Ikes a bit more roomy internally. If the GH5 is pretty much the same size as the GH4, I reckon the Ike controls could be modified to make it work, at least for video.
I forgot to mention the high tech buoyancy control system for this rig. It's an inverted bucket that keeps the unit level and neutrally buoyant mid-water, or with air removed allows it to sit firmly on the bottom or on a tripod.
Again, it doesn't look pretty but it works beautifully!
After seeing the very impressive housings on this thread I'm a little hesitant to post this, but here goes...4K on a shoestring!
The monitor (1) is a Sony CLM-V55 in a glued acrylic box - a bit of a bodgie job but it works. I use it primarily for composing shots, and it's particularly handy when the subject is on or near the bottom and the monitor can be tilted upwards.
I've fixed a couple of aluminium brackets inside the camera housing (2) to hold a 15cm HDMI adapter lead. The bracket affixed to the internal camera platform (3) has a recess to hold the camera's HDMI cover open, and also stops the male micro plug from twisting about in the camera - micro plugs can be easily damaged.
The port (4) is a 4 inch acrylic dome sourced from a US company. I reduced it to the appropriate diameter by rubbing it on fine abrasive paper placed on a flat surface, and then glued it to the barrel of a cut-down Ikelite port. The shade is made from PVC tube.
A tripod can be easily attached or removed above or below water via quick release clips on opposing sides of the affixed base (5).
Altogether this setup (Ike housing, GH4, 8mm fisheye lens and monitor) came in at around 4500 AUD (about 3600 USD), leaving a bit of change for a 55 inch UHD Sony Bravia TV.
It's not particularly pretty but it works, and the results have so far been pleasing.