The deployment of fifth generation (5G) millimetre-wave (mmWave) base stations (BSs) will consume more energy over time due to the limited time available, despite the increasing interest in developing 5G mmWave wireless communication technology. Constructing 5G mmWave cellular network infrastructure can improve energy efficiency, which is a challenge to implement in heterogeneous networks. This paper presents analytical frameworks for monitoring the effectiveness of 5G mmWave cellular networks. Based on the state management of BS, a system model for 2-tier heterogeneous networks is developed, and particle swarm optimization (PSO) is then used to compute the total energy consumption of the heterogeneous networks. Energy consumption was compared and analysed by leveraging state switching and the aggregate delay for three methods: fundamental separation, conventional separation, and a proposed energy-saving method that introduced a sleep state. Simulation shows that the proposed energy-saving method, which is a combination of conventional separation approaches, has the lowest total energy consumption and offers a 9% reduction compared to other related works. The results validate the accuracy of the power usage used in the 5G mmWave cellular network of the proposed method.