The manuscript reports on an apparently simple model that can show a five-phase equilibrium in a ternary system. The five phases are four liquids of different compositions and an ideal vapor phase. The model results from a flawed attempt to correlate the system phenol-water-n-hexane with the NRTL activity coefficient model. Experimentally, this system has three liquid phases over a range of temperatures where only the water-n-hexane binary pair shows a liquid-liquid miscibility gap. The temperature dependence used for the binary system behavior, when extrapolated, produced two separate three-phase regions, which merge as a four-phase region at a unique temperature. The fifth phase occurs at a unique pressure when an ideal gas reaches equilibrium with the four liquid phases. The model is presented as a challenging system for equilibrium computations, since many metastable equilibria with two or three phases can be found in the vicinity of the five-phase condition. The method used to obtain the computed equilibria is discussed.