You actually don't need to exit the hotel property at all, especially if the weather isn't great. The "tubes" connect the hotel to the arrivals level of Terminal 5 (via elevators) and then you can go up further to the AirTrain connecting concourse using escalators. I did this last month.
Originally Posted by
themicah
To get to the AirTrain, walk out the front of the hotel, cross the access road on the crosswalk, follow the shaded walkway to the AirTrain station, and take the elevator up to the platform. I think the total walking distance is about 500ft (the walk from the curb/AirTrain at T4 to your gate will probably be longer).
Here's a map with the walking route highlighted: