  The Hales program to prove the Kepler conjecture on sphere packings consists
of five steps, which if completed, will jointly comprise a proof of the
conjecture. We carry out step five of the program [outlined in
math.MG/9811073], a proof that the local density of a certain combinatorial
arrangement, the pentahedral prism, is less than that of the face-centered
cubic lattice packing. We prove various relations on the local density using
computer-based interval arithmetic methods. Together, these relations imply the
local density bound.
