5-Shredders in 5-connected graphs

For a graph GG, a subset SS of V(G)V(G) is called a shredder if G−SG−S consists of three or more components. We show that if GG is a 5-connected graph with |V(G)|≥135|V(G)|≥135, then the number of shredders of cardinality 5 of GG is less than or equal to (2|V(G)|−10)/3(2|V(G)|−10)/3.