This paper describes in detail the design of a 5G platform based on the C-RAN architecture, with a fully virtualized Radio Access Network (RAN) and an optical/wireless Fronthaul. The wireless and optical domains are controlled by a hierarchy of Software Defined Networking (SDN) controllers, which are responsible for endto-end optimization of the platform, including the Fronthaul and 5G air interfaces. The proposed architecture adopts a modular eNodeB (eNB) design, where virtualized BBU and RRH entities are implemented with Commercial Off-Τhe-Shelf (COTS) components. Moreover, a mmWave RAU is connected to the BBU via a feeder optical fiber, interconnecting one or more RRH units with the BBU over mmWave interfaces. COTS components and Ethernet interfaces are employed for C-RAN prototyping of our platform, facilitating flexibility, cost reduction and increased scalability.