I have a couple of ideas regarding all this.
1. The original iCloud 5.0 would not install in Windows as an update. Instead, you would get a message telling you that it would not install and suggesting you try again later, and then if that did not work to download the file and try to install it directly. The underlying cause appeared to be that iCloud 5 could not uninstall the previous version of iCloud and replace it with the update.
A lot of people tried to fix this by uninstalling iCloud 4. I was lucky, though. I did a search online and learned that everyone who had done that and were able to force iCloud 5 to install then found that the update would not work with Office 365. When I read this, I immediately changed my mind to try this procedure and decided to keep iCloud 4. Why not? I was working just fine.
2. When I got the opportunity to install Office 2016, I decided to see what happened. Nothing happened. That is, Office 2016 + Windows 10 Pro + iCloud 4.1 worked just fine. From that moment on, I just allowed each update notice from Apple to attempt an installation and didn't worry about it if it failed -- because my system was working.
However, a lot of people out there had gotten impatience and tried various fixes. Some tried down-grading their Office software; some tinkered with the system. A lot of people seemed to find some way to force an upgrade to iCloud 5.0. Unfortunately, I didn't see that anyone actually successfully got the Office-iCloud-Windows combo to work.
But, all those people had ended up with a system that now ran a corrupted combination.
3. My thought is that this resulted in a system that would not successfully upgrade to iCloud 5.1, even if it said it had. The problem would be that iCloud forced changes in its connection to Outlook, and neither was reliable any longer.
My concern would be the extent of the damage. Office is terrible at one big thing: It is almost impossible to force a clean installation. Even if you uninstall, then reinstall, it does so with all the previous settings. That ***** if you are try to fix damage you may have done to its basic setup.
The Office user info is buried deep and I have not been able to clean a previous installation even with a strong registry cleaner. Once, even an MS Tech Support member told me that the best fix to a problem I had was to zap the drive and install the entire system fresh from ground up.
Hopefully, it won't come to that for you guys.
If you think I'm right about the nature of the problem, there is what I would suggest:
a. Uninstall iCloud. (Reinstalling is cake). Use a low impact registry cleaner such as CCleaner to get rid of some of the garbage in the registry.
b. Uninstall Office. Run the registry cleaner.
c. Install Office 2013. (If you have a 365 license, MS will help you get the installer when you explain the problem).
d. Upgrade to Office 2016. With any luck, this will have cleared all the bad settings.
e. Install iCloud.
I've put things in the above order because that matches the sequence of successful installations and updates: Office 2013, Office 2016, iCloud.
I hope this works for you.