The correct, complete, and easiest answer was to take the South Exit, then walk right until you reach the Kimpton—an easy walk, even with my luggage, no complaints.Granted all I have is a piece of luggage that fits in the overhead compartment and a day pack. Wasn’t a problem on the Yamanote line either.

A JR Information desk staffer told me there were two Exit 5’s and got me going the correct way. Hopefully this saves someone else going to the Kimpton from Shinjuku some grief; it’s not bad at all if you get information other than from Google Maps which only tells you “Exit 5.”

To whoever said I “chose the wrong hotel,” I think I did fine. Got upgraded 3 room classes on a points reservation, got a late check-out, and bus 75 goes back to Shinjuku—the bus stop is on the hotel side of the road to the left.