Merry Christmas & Welcome, @Jfandrus!
I'd strongly recommend you back up all your data from the 5 TB external HDD onto the computer where the data is accessible. Afterwards, I'd strongly advise you to swap the USB cable and the USB port when connected to the problematic PC. While on it, I'd also recommend you go to
Disk Management in Windows and see how the external is recognized there. Posting some screenshots from the utility will be really helpful to me (e.g. via Imgur).
Since the issue is present on only one computer, I'd also suggest you check your USB Hub controller drivers from the motherboard/PC manufacturer's official website. You should be able to find your model there and download the latest drivers for your hardware.
Keep me posted. Hope this helps you!
SuperSoph_WD