People are always interested in solving the problem of one-dimensional nonlinear Schr?dinger equation with the fifth power. However, only a limited number of new solutions consisting of the elliptic and hyperbolic functions were obtained. In order to obtain a new infinite sequence solutions of one-dimensional nonlinear Schr?dinger equation with fifth power, it makes a series of transformations on the equation, and using the related conclusions of B?cklund transform and nonlinear superposition formula of Riccati equation the new infinite sequence solutions of one-dimensional nonlinear Schr?dinger equation with the fifth power consisting of trigonometric function, hyperbolic function and rational function were constructed.