The next-generation wireless communications require reduced energy consumption, increased data rates and better signal coverage. The millimetre-wave frequency spectrum above 30 GHz can help fulfil the performance requirements of the next-generation mobile broadband systems. Multiple-input multiple-output technology can provide performance gains to help mitigate the increased path loss experienced at millimetre-wave frequencies compared with microwave bands. Emerging hybrid beamforming architectures can reduce the energy consumption and hardware complexity with the use of fewer radio-frequency (RF) chains. Energy efficiency is identified as a key fifth-generation metric and will have a major impact on the hybrid beamforming system design. In terms of transceiver power consumption, deactivating parts of the beamformer structure to reduce power typically leads to significant loss of spectral efficiency. Our aim is to achieve the highest energy efficiency for the millimetre-wave communications system while mitigating the resulting loss in spectral efficiency. To achieve this, we propose an optimal selection framework which activates specific RF chains that amplify the digitally beamformed signals with the analogue beamforming network. Practical precoding is considered by including the effects of user interference, noise and hardware impairments in the system modelling.