The objective of the presented communication is to examine and analyze the solutions of nonlinear multi-singular fifth-order Lane–Emden (LE) system for different scenarios by variation of shape factors settled on the equivalent design of the LE equations. The neuro-evolution based stochastic computing is explored for the numerical measures using the artificial neural networks (ANNs) models for the appropriate continuous mapping, while the learning of decision variables is conducted using the integrated meta-heuristic global search of genetic algorithms (GA) hybrid with the local search efficiency of active-set (AS) i.e., ANN-GA-AS scheme. The numerical approach ANN-GA-AS is applied efficiently for the fifth kind of nonlinear LE model and statistical calculations further validate the accuracy, robustness as well as convergence.