Trajectory prediction is crucial in assisting both human-driven and autonomous vehicles. Most of the existing approaches, however, focus on straight stretches of road and do not address trajectory prediction at intersections. This work aims to fill this gap by proposing a solution that copes with the higher complexity exhibited for the intersection scenario, leveraging the 5G-MEC capabilities. In particular, the reduced latency and edge computational power are exploited to centrally collect and process measurements from both vehicles (e.g., odometry) and road infrastructure (e.g., traffic light phases). Based on such a holistic system view, we develop a Long Short Term Memory (LSTM) recurrent neural network which, as shown through simulations using a real-world dataset, provides high-accuracy trajectory predictions. The encountered challenges and advantages of the presented approach are analyzed in detail, paving the way for a new vehicle trajectory prediction methodology.