<p>The transmission dynamics of nonautonomous solitons is studied in the framework of the variable-coefficient fifth-order nonlinear Schrödinger equation, which includes besides the group-velocity dispersion and self-phase modulation terms that constitute the cubic model, the effects of fifth-order dispersion and nonlinear terms related to it. The model appertains to the description of attosecond pulse propagation in inhomogeneous optical media exhibiting higher-order dispersion. Nonautonomous soliton solutions of the bright kind are constructed analytically with the aid of similarity transformation method. It is futher emphasized that the soliton management through controlling the soliton’s velocity under the influence of the fifth-order dispersion has been explicated for the first time. Physically interesting soliton motions including the acceleration, deceleration, stopping and reversion of propagation direction, are achieved through different profiles of the varying-in-time fifth-order dispersion parameter.</p>