Fifth Generation (5G) mobile networks introduce the concept of slicing to ensure isolation among the various supported heterogeneous services. The User Equipment (UE) can be connected to multiple slices simultaneously. Additionally, the notion of a Bandwidth Part (BWP) was also instigated to reduce power consumption. A BWP is a small chunk of the bandwidth scanned by the UE to retrieve its service data. Therefore, a UE connected to multiple services can be configured with multiple BWPs each associated with a given service. Such UEs find themselves scanning multiple BWPs, which can be time consuming and highly energy intensive. Hence, it is paramount to study the appropriate choice of the BWP configuration from an energy-efficiency perspective for multi-slice users depending on their battery level. In this paper, two energy-efficient BWP selection solutions are proposed for users connected to multiple slices. The first solution is based on a centralized approach where UEs are stirred optimally to the best BWP configuration, while the second solution relies on a user-centric distributed approach using non-cooperative game theory. The proposed schemes take into account the users' battery level and their sojourn time in the network as well as the scanned BWP size. Both solutions are compared with one another and against the legacy solution. Intensive simulation results demonstrate the efficiency of our proposition in terms of usersu2019 energy efficiency and quality of service.