In the evolution of telecommunication industry towards 5G, Ethernet Passive Optical Networks (EPON) technology, with some unique features such as high capacity, low latency, and minimum cost per bit, positions itself as an interesting option for backhauling solution in the Multi-access Edge Computing (MEC) scenarios. It is expected to see the converged optical-radio nodes play a crucial role in future networks. To maximize the benefits of the 5G EPON networks, besides all other challenges, it is essential to address two main issues, namely softwarization and energy efficiency. To this end, in this paper, initially we introduce a framework to have an open control layer based on SDN (Software-Defined Networks), able to prepare the EPON backhaul to deal with the 5G applications and services. Then we introduce a solution that minimizes the energy consumption of EPON networks without imposing additional packet delay