  We present an ansatz for the planar five-loop four-point amplitude in
maximally supersymmetric Yang-Mills theory in terms of loop integrals. This
ansatz exploits the recently observed correspondence between integrals with
simple conformal properties and those found in the four-point amplitudes of the
theory through four loops. We explain how to identify all such integrals
systematically. We make use of generalized unitarity in both four and D
dimensions to determine the coefficients of each of these integrals in the
amplitude. Maximal cuts, in which we cut all propagators of a given integral,
are an especially effective means for determining these coefficients. The set
of integrals and coefficients determined here will be useful for computing the
five-loop cusp anomalous dimension of the theory which is of interest for
non-trivial checks of the AdS/CFT duality conjecture. It will also be useful
for checking a conjecture that the amplitudes have an iterative structure
allowing for their all-loop resummation, whose link to a recent string-side
computation by Alday and Maldacena opens a new venue for quantitative AdS/CFT
comparisons.
