5-Shredders in 5-connected graphs

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