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NYC was covered in a glacier the last time the global average temperature was 5C cooler.

That's not the same thing as Europe and NA cooling by 5C.

While strictly true, that doesn't mean 5C cooling wouldn't eventually result in NYC under ice.

You've misunderstood the source. While temperatures locally will drop by 5C, the global average will not.

That chart shows global averages, ie, the whole world was 5C colder. NY might have been much, much colder than that.

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.