The deployment of 5G is in full swing, with a significant yearly growth in the data traffic expected to reach 26% by the year and data consumption to reach 122 EB per month by 2022 [10]. In parallel, the idea of smart cities has been implemented by various governments and private organizations. One of the main objectives of 5G deployment is to help develop and realize smart cities. 5G can support the enhanced data delivery requirements and the mass connection requirements of a smart city environment. However, for specific high-demanding applications like tactile Internet, transportation, and augmented reality, the cloud-based 5G infrastructure cannot deliver the required quality of services. We suggest using multi-access edge computing (MEC) technology for smart cities' environments to provide the necessary support. In cloud computing, the dependency on a central server for computation and storage adds extra cost in terms of higher latency. We present a few scenarios to demonstrate how the MEC, with its distributed architecture and closer proximity to the end nodes can significantly improve the quality of services by reducing the latency. This paper has surveyed the existing work in MEC for 5G and highlights various challenges and opportunities. Moreover, we propose a unique framework based on the use of MEC for 5G in a smart city environment. This framework works at multiple levels, where each level has its own defined functionalities. The proposed framework uses the MEC and introduces edge-sub levels to keep the computing infrastructure much closer to the end nodes.