Stable set and clique polytopes of (P5P5,gem)-free graphs

STAB(G) is the convex hull of all the incidence vectors of stable sets in a graph G; CLIQUE(G) is the convex hull of all the incidence vectors of cliques in G. We give a defining linear system of STAB(G) and CLIQUE(G) when G   is a graph containing no P5P5 and no gem.