Let be a complete noncompact gradient shrinking Ricci soliton with the equation for some positive constant . In this talk, we will talk about the rigidity of five dimensional gradient shrinking Ricci soliton with constant scalar curvature. Fernández-López and García-Río (Proc. Amer. Math. Soc., 2016) proved that the scalar curvature ; if , they are finite quotient of , where is a four-dimensional Einstein manifold. If , the soliton is Einstein (Petersen-Wylie, 2009); if , it is isometric to. We proved that it is a finite quotient of if (arXiv:2411.10712); for , it is isometric to a finite quotient of under the additional condition of bounded curvature (arXiv: 2506.00887). This work is joint with Prof. Guoqiang Wu , Jianyu Ou and Yuanyuan Qu.