  We reduce all the most complicated Feynman integrals in two-loop
five-light-parton scattering amplitudes to basic master integrals, while other
integrals can be reduced even easier. Our results are expressed as systems of
linear relations in the block-triangular form, very efficient for numerical
calculations. Our results are crucial for complete next-to-next-to-leading
order quantum chromodynamics calculations for three-jet, photon, and/or hadron
production at hadron colliders. To determine the block-triangular relations, we
develop an efficient and general method, which may provide a practical solution
to the bottleneck problem of reducing multiloop multiscale integrals.
