So far I've gotten Close Combat 2 & 3 to run using compatibility mode; but Close Combat 4 & 5 refuse to function, citing 'internal errors' regardless of whatever compatibility mode, patches, or other tinkering I've attempted.

Damn. I was specifically looking for the first game, too. Oh well.

I was having the issue with the game running too fast but it looks like there is an easy fix for this.

Click Options at the Top
Go to Preferences
Change Game Speed from Fastest(Which seems to be default) to something like Medium.

Now the battle isn't over in the blink of an eye.

Not sure if running the compatibility troubleshooter helped as well but the main issue of the game running too fast was solved by the preference option. Everything else for CC1 runs fine on Win10 x64

The only thing that is annoying is that each time you right-click you're thrown into the browser, as that button enables the in-game help, which doesn't work anymore in Windows 10, so it goes to some Microsoft help page that says this. Is there some way to unbind this button or to make the help work properly besides running it on an older version of Windows natively or in a Virtual machine where .hlp files are still supported?

They are running all of them without problem here