The next generation of mobile networks, 5G, aims at supporting lower end-to-end latency, higher reliability and higher throughput, which can be improved by MEC and multi-RAT offloading, respectively. With MEC, a base station in 5G can be equipped with computing power, which can be called as an edge in MEC. With the assistance of the edges, traffic with computational tasks can be directly executed in local servers, without forwarding the tasks to the cloud or core network. Edge computing hence reduces the latency and the traffic load significantly. Conventional multi-RAT offloading decides based only on either communication resources or computing resources. In this work, we argue that, to better utilize the communication and computing resources, neighboring edges should share their resources and cooperatively offload the requests from their clients. To this end, we introduced a double offloading mechanism, called LCCOP, to offload incoming traffic to the best pair of radio and edge subject to the end-to-end latency of the requesting connections. We conduct simulations to compare LCCOP with the conventional offloading schemes. The results show that LCCOP's double offloading can significantly improve the satisfaction ratio by up to 83 percent and 143 percent, respectively, as compared to pure computation offloading and pure communication offloading.