  We compute the two-loop four-point form factor of a length-3 half-BPS
operator in planar N=4 SYM, which belongs to the class of two-loop five-point
scattering observables with one off-shell color-singlet leg. A new
bootstrapping strategy is developed to obtain this result by starting with an
ansatz expanded in terms of master integrals and then solving the master
coefficients via various physical constraints. We find that consistency
conditions of infrared divergences and collinear limits, together with the
cancellation of spurious poles, can fix a significant part of the ansatz. The
remaining degrees of freedom can be fixed by one simple type of two-double
unitarity cut. Full analytic results in terms of both symbol and Goncharov
polylogarithms are provided.
