This paper addresses the new concatenation model incorporating quintic-order dispersion, incorporating four well-known nonlinear models. The concatenated models are the nonlinear Schr¨odinger equation, the Hirota equation, the Lakshmanan-Porsezian-Daniel equation, and the nonlinear Schr¨odinger equation with quintic-order dispersion. The model itself is innovative and serves as an encouragement for investigating and analyzing the extracted optical solitons. These models play a crucial role in nonlinear optics, especially in studying optical fibers. Three integration algorithms are implemented to investigate the optical solitons with the governing model. These techniques are the Weierstrass-type projective Riccati equation expansion method, the addendum to Kudryashov’s method, and the new mapping method. The solutions obtained include various solitons, such as bright, dark, and straddled solitons. Additionally, the paper reports hyperbolic solutions and Weierstrass-type doubly periodic solutions. These solutions are novel and have never been reported before. Visual depictions of some selected solitons illustrate these solutions’ dynamic behavior and wave structure.