Energy consumption is a critical issue for the communications network operators, impacting deeply the cost of the services, as well as the ecological footprint. Network slicing architecture for 5G mobile communications enables multiple independent virtual networks to be created on top of a common shared physical infrastructure. Each network slice needs different types of resources, including energy, to fulfill the demands requested by each application, operator, or vertical market. The existing literature on network slicing is mainly targeted at the partition of network resources; however, the corresponding management of energy consumption is an unconsidered critical concern. This paper analyzes the requirements for an energy-aware 5G network slicing provisioning according to the 3GPP specifications, proposes an architecture, and studies the strategies to provide efficient energy consumption in terms of renewable and non-renewable sources. NFV and SDN technologies are the essential enablers and leverage the Internet of Things (IoT) connectivity provided by 5G networks. This paper also presents the technical 5G technology documentation related to the proposal, the requirements for adaptive energy management, and the Integer Linear Programming (ILP) formulation of the energy management model. To validate the improvements, an exact optimal algorithmic solution is presented and some heuristic strategies.