The Caudrey-Dodd-Gibbon (CDG) equation, a core constituent of the fifth-order Korteweg-de Vries (KdV)-type nonlinear wave equations, possesses exact solutions that are of pivotal significance for elucidating the mechanisms of wave propagation under the coupling effect of strong dispersion and intense nonlinearity. To mitigate the limitations inherent in traditional analytical methods for solving such high-order equations—encompassing narrow applicability, high computational complexity, and expression explosion a Feature-Enhanced Direct Symbolic Computation Neural Network(FEDSCNN) algorithm is proposed. This algorithm integrates the adaptive feature extraction capability of neural networks, the rigor of symbolic computation, and the advantages of feature enhancement. It constructs single-hidden-layer "2-5-3-1" and double-hidden-layer "2-5-2-2-1" architectures, and obtains exact solutions through a sequence of steps, namely symbolic derivation, equation mapping transformation, and constraint system solving.Experimental results validate that the proposed algorithm successfully acquires multiple categories of solitary wave solutions and periodic solutions for the CDG equation, with a zero error margin corroborated by the Maple symbolic computation engine. Furthermore, this algorithm circumvents the necessity of presetting solution forms, attains a higher convergence rate, and exhibits enhanced capability in capturing high-order terms. The present study not only furnishes an efficient and innovative approach for solving the CDG equation but also provides a general framework for the analytical solution of analogous high-order nonlinear wave equations, thereby facilitating the interdisciplinary integration of neural networks and symbolic computation.