Multi-access edge computing (MEC) is a new leading technology for meeting the demands of key performance indicators (KPIs) in 5G networks. However, in a rapidly changing dynamic environment, it is hard to find the optimal target server for processing offloaded tasks because we do not know the end users’ demands in advance. Therefore, quality of service (QoS) deteriorates because of increasing task failures and long execution latency from congestion. To reduce latency and avoid task failures from resource-constrained edge servers, vertical offloading between mobile devices with local-edge collaboration or with local edge-remote cloud collaboration have been proposed in previous studies. However, they ignored the nearby edge server in the same tier that has excess computing resources. Therefore, this paper introduces a fuzzy decision-based cloud-MEC collaborative task offloading management system called FTOM, which takes advantage of powerful remote cloud-computing capabilities and utilizes neighboring edge servers. The main objective of the FTOM scheme is to select the optimal target node for task offloading based on server capacity, latency sensitivity, and the network’s condition. Our proposed scheme can make dynamic decisions where local or nearby MEC servers are preferred for offloading delay-sensitive tasks, and delay-tolerant high resource-demand tasks are offloaded to a remote cloud server. Simulation results affirm that our proposed FTOM scheme significantly improves the rate of successfully executing offloaded tasks by approximately 68.5%, and reduces task completion time by 66.6%, when compared with a local edge offloading (LEO) scheme. The improved and reduced rates are 32.4% and 61.5%, respectively, when compared with a two-tier edge orchestration-based offloading (TTEO) scheme. They are 8.9% and 47.9%, respectively, when compared with a fuzzy orchestration-based load balancing (FOLB) scheme, approximately 3.2% and 49.8%, respectively, when compared with a fuzzy workload orchestration-based task offloading (WOTO) scheme, and approximately 38.6%% and 55%, respectively, when compared with a fuzzy edge-orchestration based collaborative task offloading (FCTO) scheme.