The Ramsey numbers of fans versus a complete graph of order five

For two given graphs F and H, the Ramsey number R(F, H) is the smallest integer N such that for any graph G of order N, either G contains F or the complement of G contains H. Let F-l denote a fan of order 2l + 1, which is l triangles sharing exactly one vertex, and K-n a complete graph of order n. Surahmat et al. conjectured that R(F-l,F- K-n) = 2l (n - 1) + 1 for l >= n >= 5. In this paper, we show that the conjecture is true for n = 5.