Pushing the reach of NNLO QCD predictions to $2\to3$ production processes is one of
the pillars of precision phenomenology program at the LHC. In this talk we will
overview recent results and developments in the calculation of two-loop five-point
amplitudes contributing towards achieving this goal. We will discuss challenges
encountered in advancing the state-of-the-art beyond the class of massless
five-point scattering. We will then present a basis set of transcendental
functions sufficient to express any planar two-loop five-particle scattering
amplitude with one external massive leg. This basis greatly facilitates
derivation of compact analytic form of scattering amplitudes, and opens a
possibility of their fast and reliable numerical evaluation. Applications for
phenomenology of electroweak boson production can be reasonably anticipated in
the near future.