If you've upgraded to Plasma 5, you'll want to:

1. First get rid of the broken new default clipboard manager which is very similar to Klipper. Sorry, I forgot how I managed that, but it's possible.
2. Start Klipper
3. Finally, get Klipper to start automatically... which is also non-trivial. To achieve that, exit Klipper, and when asked whether Klipper should start automatically, obviously agree.
4. If you're like me, enable Synchronize contents of the clipboard and the selection

And that, my friend, completes the path to go back to an experience as sane as KDE 4, at least in clipboard terms... if you manage to get Ctrl+Alt+V to bring up Klipper, and accept that selecting text using the keyboard will update the clipboard.