With the advent of technologies such as Edge computing, the horizons of remote computational applications have broadened multidimensionally. Autonomous Unmanned Aerial Vehicle (UAV) mission is a vital application to utilize remote computation to catalyze its performance. However, offloading computational complexity to a remote system increases the latency in the system. Though technologies such as 5G networking minimize communication latency, the effects of latency on the control of UAVs are inevitable and may destabilize the system. Hence, it is essential to consider the delays in the system and compensate for them in the control design. Therefore, we propose a novel Edge-based predictive control architecture enabled by 5G networking, PACED-5G (Predictive Autonomous Control using Edge for Drones over 5G). In the proposed control architecture, we have designed a state estimator for estimating the current states based on the available knowledge of the time-varying delays, devised a Model Predictive controller (MPC) for the UAV to track the reference trajectory while avoiding obstacles, and provided an interface to offload the high-level tasks over Edge systems. The proposed architecture is validated in two experimental test cases using a quadrotor UAV.