Atomistic modeling of CoCrFeNiMn (0 < x_Mn <25 at %) high entropy alloys shows that the melting temperature as a function of Mn concentration does not follow the behavior consistent with a homogeneous solid solution, exhibiting a maximum value for 8.7 at % Mn. Using the concepts of the BFS method for alloys, a description of the phenomenon is provided, showing that sluggish diffusion generates changes in the atomic distribution that lead to this anomalous behavior. This theoretical analysis is meant to provide a template for studying complex compositions and fine effects in high entropy alloys, which would be hard to detect experimentally but that could have an impact on potential applications of these complex materials.