The Ave Temp of the world is rising and from what I read and hope I understood, nothing will really stop that, all we can do is hope to lessen the temp rise.
So, I think this "5C" drop in East NA and West Europe will be absorbed throughout the world. So those regions will still have higher ave temp then say 1950, just a bit less than the rest of the world.
Which for reference a 5C drop should mean that New York is covered in glacier according to this source https://xkcd.com/1732/