Does the Mac mini with M1 support the LG 5k display?

So far, it does not. Just connected my new M1 to my LG Ultrafine 5k and it blanks out randomly despite using the same connection that works fine with my 2018 Macbook Pro and despite the M1 Mini driving a 4k VewSonic (HDMI) without any issues (which looks quite nice, but would prefer to be able to use the 5K and its built in camera.

I have a mini M1 and an LG 4K Ultrafine. I first connected the display with an OWC Thunderbolt cable, and had problems waking the display. I bought an Apple Thunderbolt Cable (0.8 m) and that fixed all problems. So any problems may not be with the devices on each end !