The Ramsey number r(K5 - P3, K5)

For two given graphs G(1) and G(2), the Ramsey number r(G(1), G(2)) is the smallest integer n such that for any graph G of order n, either G contains G(1) or the complement of G contains G(2). Let K-m denote a complete graph of order m and K-n - P-3 a complete graph of order n without two incident edges. In this paper, we prove that r(K-5 - P-3, K-5) = 25 without help of computer algorithms.