<p>A significant challenge for networks in 5G and beyond is their high energy consumption, which is caused by the high-density overlapping heterogeneous cellular network architecture. Thus, energy efficiency is a critical factor to take into account during the design and operation of 5G and beyond networks. Nevertheless, energy wastage that occurs during periods of minimal traffic can be mitigated by employing the sleep mode on the base station. In this work, we presented a design of a Cognitive Radio Network (CRN) by implementing an energy-saving scheme based on sleep mode, modeled using a discrete-time multi-server priority queue. The present study aims to develop and evaluate an energy-saving scheme for unreliable and heterogeneous Cognitive radio networks. The system is modeled as a five-dimensional Markov chain and transiently analyzed using the Recursive method. Then, using the transient probability vector, we derived the numerical result based on queueing analysis and reliability analysis to validate our proposed model. The results, depending on the degree of energy-saving, are presented to demonstrate the efficacy of the proposed scheme. In addition, simulation experiments are performed to corroborate the accuracy and validity of the numerical results. Moreover, a sensitivity analysis of various performance metrics, along with the degree of energy savings, is performed using the Monte Carlo simulation with the correlation-based method. Finally, we implemented a multi-objective optimization approach for the reward cost and the degree of energy savings and achieved a Pareto solution.</p>