Traffic on future fifth-generation (5G) mobile networks is predicted to be dominated by challenging video applications such as mobile broadcasting, remote surgery and augmented reality, demanding real-time, and ultra-high quality delivery. Two of the main expectations of 5G networks are that they will be able to handle ultra-high-definition (UHD) video streaming and that they will deliver services that meet the requirements of the end user's perceived quality by adopting quality of experience (QoE) aware network management approaches. This paper proposes a 5G-QoE framework to address the QoE modeling for UHD video flows in 5G networks. Particularly, it focuses on providing a QoE prediction model that is both sufficiently accurate and of low enough complexity to be employed as a continuous real-time indicator of the "health" of video application flows at the scale required in future 5G networks. The model has been developed and implemented as part of the EU 5G PPP SELFNET autonomic management framework, where it provides a primary indicator of the likely perceptual quality of UHD video application flows traversing a realistic multi-tenanted 5G mobile edge network testbed. The proposed 5G-QoE framework has been implemented in the 5G testbed, and the high accuracy of QoE prediction has been validated through comparing the predicted QoE values with not only subjective testing results but also empirical measurements in the testbed. As such, 5G-QoE would enable a holistic video flow self-optimisation system employing the cutting-edge Scalable H.265 video encoding to transmit UHD video applications in a QoE-aware manner.