I also have a business hp elite notebook (approx. 3 - 4 years old). Can't install any software either. Monitor was recognised with win10 and now win11 without any problems. Only the full resolution can the older hp notebook not yet with 60hz, but in the intel graphics driver, which is fortunately not blocked by our it, I could set the full resolution in 30 hz. I wouldn't want to miss the full 5k resolution for office and programming. At the beginning, I had problems with the recognition, but that was due to the usb3 cable that came with the monitor. I have now bought a 1.5m long one and it works without any problems.

I did a quick search, but I'm not sure which version you have.(https://support.hp.com/us-en...) If it can do 4K at 60Hz, it can probably do 5K at 30Hz. If you use the screen as a split screen in the ratio 80/20, it should be able to display 4K at 60Hz.
Important: I would highly recommend the DEll Display Manager software, especially if you connect more than 1 source. (I would definitely check with IT whether they can/are allowed to install it).

My company laptop Lenovo T470 with Windows 10 does not recognise the mouse or Ethernet of the Dell monitor when I connect it via Thunderbolt. I have only found drivers for colour profiles at Dell, not for the docking station. What works via TB is the full resolution, but only at 30Hz. This doesn't bother me much because I already have a docking station. My PC recognises the KVM switch, including mouse and Ethernet. It should also be noted that the Ethernet port can only be used by the active device, which is another reason for me not to use the internal KVM. I am very satisfied with the monitor itself.