The introduction of fifth-generation (5G) mobile networks leads to an increase in energy consumption and higher operational costs for mobile network operators (MNOs). Consequently, the optimization of 5G networks' energy efficiency is crucial, both in terms of reducing MNO costs and in terms of the negative environmental impact. However, many aspects of the 5G mobile network technology itself have been standardized, including the 5G network slicing concept. This enables the creation of multiple independent logical 5G networks within the same physical infrastructure. Since the only necessary resources in 5G networks need to be used for the realization of a specific 5G network slice, the question of whether the implementation of 5G network slicing can contribute to the improvement of 5G and future sixth-generation networks' energy efficiency arises. To tackle this question, this review paper analyzes 5G network slicing and the energy demand of different network slicing use cases and mobile virtual network operator realizations based on network slicing. The paper also overviews standardized key performance indicators for the assessment of 5G network slices' energy efficiency and discusses energy efficiency in 5G network slicing lifecycle management. In particular, to show how efficient network slicing can optimize the energy consumption of 5G networks, versatile 5G network slicing use case scenarios, approaches, and resource allocation concepts in the space, time, and frequency domains have been discussed, including artificial intelligence-based implementations of network slicing. The results of the comprehensive discussion indicate that the different implementations and approaches to network slicing pave the way for possible further reductions in 5G MNO energy costs and carbon dioxide emissions in the future.