Precise theoretical predictions for 2โ3 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 2โ3 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.