<p>Energy efficiency in cellular networks has recently received more attention due to its environmental benefits and operational cost reductions. Also, the third-generation partnership project’s new radio specification aims to reduce energy consumption and greenhouse gas emissions in fifth-generation (5G) and future networks, supporting information and communication technology (ICT) sustainability targets. In this article, advanced sleep mode (ASM) as an energy-saving approach is proposed for the cognitive radio networks (CRN) of 5G and future networks, in which base station (BS) progressively enters into profound and less energy-consuming states during inoperative periods. In addition, the energy-saving approach is implemented on the heterogeneous and unreliable CRN using the discrete-time MAP/PH/1 priority G-queue model. Then, by modeling the entire system as a three-dimensional Markov chain, we conduct the system’s transient and steady-state analysis using the recursive and matrix analytic methods, respectively. So, in this work, high-performance computing is employed to efficiently handle large-scale matrix operations involving numerous states at the base station under heterogeneous CRN traffic. Thereafter, we randomly simulate the numerical results of various performance metrics with the transient and steady-state probability vector to provide validation of the proposed model as well as a comparison with the existing models. From the comparison plots, we present the impact of modeling CRN with the MAP/PH/1 queue model and the effect of reliability on the system’s performance metrics. Subsequently, a sensitivity analysis of the degree of energy savings is performed using the Monte Carlo simulation with a correlation-based method. Finally, a multi-objective analysis is carried out to explore the trade-off between the system’s quality of service and the degree of energy savings using Non-dominated Sorting Genetic Algorithm II and Multi-Objective Particle Swarm Optimization techniques.</p>