Hello RandomBelgian, welcome aboard!
Here is the fix to your issue:
https://www.subsim.com/radioroom/sho...&postcount=452
All you have to do is replace the original SH5.exe with the new SH5.exe THEBERBSTER provided, then set up your Ubisoft settings to those shown in the pictures.
When you replace the original SH5.exe with the new SH5.exe Peter provided, you are thus completely removing Ubisoft from the game which means pesky Ubisoft won't ask for your game key.
Though it is advised to do this BEFORE installing TWoS, I did it after installing it and it worked fine for me. You can do whatever you choose, however.