MAPPINGS V is a update of the MAPPINGS code (ascl:1306.008) and provides new cooling function computations for optically thin plasmas based on the greatly expanded atomic data of the CHIANTI 8 database. The number of cooling and recombination lines has been expanded from ~2000 to over 80,000, and temperature-dependent spline-based collisional data have been adopted for the majority of transitions. The expanded atomic data set provides improved modeling of both thermally ionized and photoionized plasmas; the code is now capable of predicting detailed X-ray spectra of nonequilibrium plasmas over the full nonrelativistic temperature range, increasing its utility in cosmological simulations, in modeling cooling flows, and in generating accurate models for the X-ray emission from shocks in supernova remnants.