Precise theoretical predictions for 2→3 processes are indispensable for the ongoing precision phenomenology program at the LHC and are on the current edge of NNLO QCD calculations. In this talk, I will first overview the recent advances in the challenging calculations of two-loop corrections for massless five-point scattering that paved the way for phenomenological applications. I will then present fully-differential NNLO QCD corrections to the production of three isolated photons at hadron collides, the first 2→3 process for which NNLO corrections have been calculated. The calculation is performed employing an implementation of qT-subtraction formalism within MATRIX, and the recent analytic results for the two-loop amplitudes. The NNLO QCD corrections for triphoton production are large and they are essential to describe the experimental measurements. Understanding the apparent lack of perturbative convergence of the fixed-order predictions for this process is therefore indispensable.