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In this paper, we have established the (G'/G)-expansion method to find exact solutions for time fractional fifth-order Caudrey-Dodd-Gibbon equation (FCDG5). This method is an effective method in finding exact traveling wave solutions of nonlinear evolution equations (NLEEs) in mathematical physics. The present approach has the potential to be applied to other nonlinear fractional differential equations. All of the numerical calculations in the present study have been performed on a PC applying some programs written in Mathematica.