  Using the method of maximal cuts, we construct the complete D-dimensional
integrand of the five-loop four-point amplitude of N = 4 super-Yang-Mills
theory, including nonplanar contributions. In the critical dimension where this
amplitude becomes ultraviolet divergent, we present a compact explicit
expression for the nonvanishing ultraviolet divergence in terms of three vacuum
integrals. This construction provides a crucial step towards obtaining the
corresponding amplitude of N = 8 supergravity useful for resolving the general
ultraviolet behavior of supergravity theories.
