Fall prevalence is high among elderly people, which is challenging due to the severe consequences of falling. This is why rapid assistance is a critical task. Ambient assisted living (AAL) uses recent technologies such as 5G networks and the internet of medical things (IoMT) to address this research area. Edge computing can reduce the cost of cloud communication, including high latency and bandwidth use, by moving conventional healthcare services and applications closer to end-users. Artificial intelligence (AI) techniques such as deep learning (DL) have been used recently for automatic fall detection, as well as supporting healthcare services. However, DL requires a vast amount of data and substantial processing power to improve its performance for the IoMT linked to the traditional edge computing environment. This research proposes an effective fall detection framework based on DL algorithms and mobile edge computing (MEC) within 5G wireless networks, the aim being to empower IoMT-based healthcare applications. We also propose the use of a deep gated recurrent unit (DGRU) neural network to improve the accuracy of existing DL-based fall detection methods. DGRU has the advantage of dealing with time-series IoMT data, and it can reduce the number of parameters and avoid the vanishing gradient problem. The experimental results on two public datasets show that the DGRU model of the proposed framework achieves higher accuracy rates compared to the current related works on the same datasets.