The upcoming fifth generation (5G) of mobile communications brings new paradigms, such as network slicing and automation, to the forefront. Cloud computing and network function virtualization (NFV) constitute two fundamental key enablers towards the implementation of these new paradigms. On the one hand, computational functionalities are no longer limited to distant servers, but they are coming closer to the end user through Multi-access Edge Computing (MEC) technology, thus creating a multi-tier cloud architecture in modern networks. On the other hand, going beyond the existing rigid architectures, NFV enables the flexible and on-the-fly creation and placement both of application and network functions, aiming at satisfying the diverse application requirements and optimizing the management of the heterogeneous (network, computational and storage) resources. In this paper, we discuss the challenges that arise in a MEC-enabled 5G architecture that supports the flexible placement/migration of network and application virtual network functions (VNFs), orchestrated by an NFV Orchestrator (NFVO) with admission management functionalities, able to manage on-the-fly the network functions and resources. Finally, we describe in detail a MECenabled testbed architecture that facilitates the development and testing of such solution in the context of 5G networks.