I run Ubuntu 16.04 using kde and plasma 5.8.5. I created a new activity, it let me create it, give it a name etc and it shows up in the activity manager but nothing I do switches to it. I click on it, create a hotkey shortcut for it etc and nothing. Are activities broken in plasma 5.8.5?

I would hope not as Activities are a core feature of Plasma.
My first suspicion is that when you created the new activity it may have switched you to it without you realizing. You can test this by changing the background in the current activity and then check the Activity switcher to see which activity's background changed. Some other things to try: switch back and forth between each of your activities, log out and back in and try again, create a new user and test things with that user.

Some Screenshots of what you are seeing may be helpful in figuring out what's going on.