The 5G network technology is a promising technology that can successfully meet the demand for network capacity growth, due to its high-speed, low-latency, and wide connectivity capabilities. Adapting 5G will increase the energy consumption and CO2 emissions caused by this high consumption. Base stations (BSs) consume the most power in mobile networks accounting for approximately 57% of total energy consumption. This study proposes an integrated meta-heuristic optimization algorithm that combines the Arithmetic Optimization Algorithm (AOA) and the Particle Swarm Optimization (PSO) method. This combination aims to leverage the strengths of both approaches improving the speed and accuracy of the optimization process, to achieve better energy efficiency (EE) in 5G network technology. The proposed algorithm performance is evaluated based on a set of benchmarks functions and compared with other optimization methods. And to demonstrate the applicability of the proposed algorithm in terms of network energy efficiency problem, it was tested against a real-world case study involving power allocation in 5G, the results showed that the proposed algorithm outperforms more recent meta-heuristics state-of-the-art methods in solving a wide range of benchmark functions and obtaining a fair power allocation for multiple users in 5G network. Moreover, it maximizes energy efficiency while maintaining users service quality and availability and reducing total network energy consumption.