Cell sizes of the Fifth Generation (5G) of mobile networks grow inexorably smaller because of the massive Multiple-Input Multiple-Output (MIMO) and millimeter wave communication technologies to be used. It is therefore challenging to address the mobility management, especially vertical handover in 5G networks. In this paper, an intelligent vertical handover framework is proposed and discussed to simplify the network selection, and to reduce the handover latency and frequency. Integrating Media-independent handover (MIH) and Software-defined network (SDN) technologies, the core of our design is to ensure the handover happens between only two potential networks regardless of the available types of technologies. For this purpose, we exploit three types of handover information with a new pre-selection scheme to eliminate unqualified networks and generate a network ranking. Moreover, with the introduction of steady period, we use the feature of SDN to deliver the best two candidate networks to the two-dimensional (2D) cost function module for the final decision. Simulation results show that our proposed framework can accurately select the optimal network in an efficient manner even if a number of access technologies exist. Furthermore, our framework reduces the vast backhaul traffic during a vertical handover process and keeps the backhaul energy consumption low. Eventually, simulation also shows superiority when the cell sizes are diverse.