I am looking for sport cams to put on my 5". I found one of those Polaroid cubes for $30 somewhere, not sure if that is good for it. Not that into vlogging or anything media type, so I don't need a super expensive go pro or something
DJI Osmo Action 4 has been super solid for me. Excellent quality, can record 10-bit D-Log M, and great low-light performance for about half the price of a Go Pro. Alternatively, the Runcam Thumb Pro 4k v2 (or Runcam Thumb Pro W, name varies depending on where you're buying it) is a great budget action cam.
Supposed to be pretty durable. Comes with a cage but it doesn't offer a ton of extra protection intrinsically and connects to the mount via a magnetized clip which I would imagine cant really withstand a really hard crash without launching the camera and cage - I recommend a more solid custom mount with additional protection. It comes stock with one 1800mah (IIRC) battery but you can find 2100mah off brands super cheap. I am pretty sure that you can power it through your balance lead with a 5v converter and USB C rig.