The current article aims to analytically solve the conformable space-time fractional Fokas (CSTFF) equation in (4+1) dimensions. The new sub-equation method is applied to achieve this purpose. First, the fractional wave transformation reduces the equation to an integer-order ordinary differential equation (ODE). After the homogeneous balance of the ODE terms, a set of algebraic equations is considered. Five cases of solutions of the group of algebraic equations are obtained with the aid of the Maple tool. Studying the five solutions cases, we get twelve solutions families for every case. The results confirm that the new sub-equation method is efficient for analyzing various solutions of nonlinear conformable time-fractional partial differential equations.