Service function chain (SFC) plays a prominent role in realizing 5G Slicing and next generation networks. Supported by the emerging techniques such as Software-Defined Networking (SDN) and Network Function Virtualization (NFV), network operators can freely define and configure a variety of complex network services or SFCs based on business needs, policies, and quality of service (QoS) requirements. Additionally, 5G networks are expected to be highly dynamic, constantly upgrading and scaling, in which case a plug-and-play mechanism is needed to avoid high operational and management costs, for which the flexible and scalable distributed system is well suited. This thesis investigates the distributed SFC provisioning problem, and propose a fully distributed algorithm that runs with dynamic traffic aiming to find and reserve the best suited network and compute resources for each SFC request with manageable messaging costs. We implemented the resulting algorithm in the OMNET++ environment and conducted a series of experiments with different dynamic traffic instances running on a distributed network. We then compare its performance with a classical centralized resource constraint shortest path (RCSP) algorithm, the results show that our 5G provisioning algorithm obtains a similar performance to the centralized RCSP in terms of throughput and acceptance rate.