  We present the analytic form of all leading-color two-loop five-parton
helicity amplitudes in QCD. The results are analytically reconstructed from
exact numerical evaluations over finite fields. Combining a judicious choice of
variables with a new approach to the treatment of particle states in $D$
dimensions for the numerical evaluation of amplitudes, we obtain the analytic
expressions with a modest computational effort. Their systematic simplification
using multivariate partial-fraction decomposition leads to a particularly
compact form. Our results provide all two-loop amplitudes required for the
calculation of next-to-next-to-leading order QCD corrections to the production
of three jets at hadron colliders in the leading-color approximation.
