With the progress of network technology in recent years, multimedia streaming applications have become increasingly popular. However, it is difficult to achieve quality of service and efficiency for multimedia streaming over vehicular networks because of the high mobility feature. Over the existing network architecture, it is difficult to immediately analyze the status of the entire network, and then establish the rules of allocation and management. However, the novel network architecture, software-defined networking, offers other options for making network management more efficient, especially for the 5G network environment. Hence, a buffer-aware streaming approach is proposed to allow users to play multimedia streaming over vehicular 5G networks, in the case of handover between different eNodeBs, to achieve minimum delay and have better quality of service. According to the user's mobility information, the status of the player buffer, and the current strength of the network signal, the proposed approach can provide the transmission strategy of multimedia streaming to the SDN controller. Finally, the experimental results proved that the proposed approach is able to not only adjust the priority of streaming content segments with the buffer and mobility status of user equipment to effectively retain overall streaming services quality, but also avoid the delay of streaming content transmission for 5G vehicular networks.