The topology of phase diagrams of five-component systems with stoichiometric compounds in the subsolidus region was studied using graph theory. A set of four classification features for such diagrams was proposed. This set served as the basis for developing a classification of this type of phase diagram; an algorithm for their construction and enumeration is presented. A set of four-dimensional homogeneous polytopes was formed, comprising polytopes having seven through 10 vertices, in order to construct all isobaric-isothermal subsolidus sections of five-component systems. Exemplary classification and construction are given, as well as an enumeration table, for the phase diagrams of systems containing up to three compounds of different types. The results of the work can appear helpful to optimize experimental studies of phase diagrams of five-component systems, as well as to develop databases on phase diagrams.