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Mobile edge computing (MEC) is a promising paradigm to provide cloud-computing capabilities in close proximity to mobile devices in fifth-generation (5G) networks. In this paper, we study energy-efficient computation offloading (EECO) mechanisms for MEC in 5G heterogeneous networks. We formulate an optimization problem to minimize the energy consumption of the offloading system, where the energy cost of both task computing and file transmission are taken into consideration. Incorporating the multi-access characteristics of the 5G heterogeneous network, we then design an EECO scheme, which jointly optimizes offloading and radio resource allocation to obtain the minimal energy consumption under the latency constraints. Numerical results demonstrate energy efficiency improvement of our proposed EECO scheme.