Five-loop four-point amplitude of N<format >=<format >4 super-yang-mills theory

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 required to resolve the general ultraviolet behavior of supergravity theories.