This paper investigates the propagation of quiescent optical solitons in magneto-optic waveguides governed by Kudryashov's quintuple power-law of self-phase modulation, incorporating generalized temporal evolution and nonlinear chromatic dispersion. The governing model accounts for the interplay between higher-order nonlinear effects and dispersive properties, which are essential for understanding the complex dynamics of light in structured optical media. To obtain exact soliton solutions, we employ the direct algebraic method and an advanced version of the sub-ODE approach, providing a robust analytical framework for recovering a wide spectrum of soliton profiles. The derived solutions include bright, dark, and singular soliton structures. Additionally, numerical simulations are conducted to verify and illustrate the physical relevance of the analytical results, demonstrating the stability and dynamical behavior of the solitons under varying parametric conditions. The findings contribute to the theoretical foundation of magneto-optic waveguide systems and offer potential applications in advanced photonic technologies and optical communication systems.