Smart devices in Industry 5.0, such as sensors and robots, are often limited by low battery life and finite computational resources, hindering their ability to perform complex tasks. By offloading computation-intensive tasks to Mobile Edge Cloud Computing (MEC) servers at the network’s edge, businesses can achieve real-time data processing and analysis, reducing communication latency, quicker response times, and improved system reliability. This work presents an integrated framework for MEC and Industry 5.0, aimed at enhancing the performance, efficiency, and flexibility of industrial processes. In particular, we propose a joint optimization problem that maximizes computational energy efficiency by optimally allocating resources, such as processing power and computational resources, as well as device association, in the most efficient manner possible. The problem is formulated as nonconvex/nonlinear, which is intractable and poses high complexity. To solve this challenging problem, we first transform and decouple the original optimization problem into a series of subproblems using the block coordinate descent method. Then, we iteratively obtain an efficient solution using convex optimization methods. In addition, our work sheds light on the fundamental trade-off between local computation and partial offloading schemes. The results show that for small data size requirements, the performance is comparable among different schemes. However, as data size increases, our proposed hybrid scheme, which includes a partial offloading scheme, outperforms others, highlighting the effectiveness of the proposed joint optimization scheme.