An edge of a k-connected graph is said to be k-contractible if the contraction of the edge results in a k-connected graph. A graph H is said to be a forbidden subgraph for k-contractible edges if every k-connected graph with no subgraph isomorphic to H has a k-contractible edge. Kawarabayashi showed that if k is an odd integer such that k≥ 5, then K 1+(P 3∪ K 2) is a forbidden subgraph for k-contractible edges. We present a new forbidden subgraph for 5-contractible edges which has K 1+(P 3∪ K 2) as a subgraph. This is an extension of the previous result in 5-connected case.