Smart manufacturing systems act as a major transformation from Industry 4.0 to 5.0 through AI-driven, trustworthy approaches in a sustainable way. Existing advanced technologies, such as the Industrial Internet of Things (IIoT) and edge computing, have enhanced productivity and efficiency in manufacturing. However, operational response time, data privacy and transparency in multi-modal systems are major disadvantages in intelligent manufacturing architecture. This study demonstrated the intelligent technologies, integrated frameworks and their existing challenges through an IIoT-based multi-agent system in manufacturing. To enhance the prediction accuracy and reliability and reduce unplanned downtime, an integrated framework is proposed for explainable multi-agent federated edge-AI (EMFEA) for a sustainable smart manufacturing system. The core technologies, such as collaborative multi-agent systems, federated learning with privacy protection, and their synergistic integration in manufacturing, are examined through this intelligent EMFEA system. A CNN-driven predictive model is utilised to drive an adaptive closed-loop control strategy to execute the real-time optimisation of critical manufacturing (specifically machining) parameters, such as energy consumption, heat input and tool path, that achieves superior performance compared to conventional ML approaches. At the end, the major challenges of this proposed approach and future research directions to adopt such a system are examined through system-level analysis. This FMFEA approach can help to ensure reliable, resilient and adaptive manufacturing practices in the Industry 5.0 era.