The 'E' train runs up 8th Avenue and turns to the east at 53d Street. It is fast when running express, but that may not apply in your case: leaving Manhattan at 5:30am would cut it rather close.

In any case, remember to get a cash-value Metrocard for the trip: each one-way trip between JFK and Manhattan requires $7 in face value. At AirTrain, you swipe upon exit, at the subway, upon entrance.

The A train will be running infrequently for the next several years (!) because of an equipment room fire this past weekend.

More information HERE