Federated Learning (FL) has been recently proposed as an emerging paradigm to build machine learning models using distributed training datasets that are locally stored and maintained on different devices in 5G networks while providing privacy preservation for participants. In FL, the central aggregator accumulates local updates uploaded by participants to update a global model. However, there are two critical security threats: poisoning and membership inference attacks. These attacks may be carried out by malicious or unreliable participants, resulting in the construction failure of global models or privacy leakage of FL models. Therefore, it is crucial for FL to develop security means of defense. In this article, we propose a blockchain-based secure FL framework to create smart contracts and prevent malicious or unreliable participants from involving in FL. In doing so, the central aggregator recognizes malicious and unreliable participants by automatically executing smart contracts to defend against poisoning attacks. Further, we use local differential privacy techniques to prevent membership inference attacks. Numerical results suggest that the proposed framework can effectively deter poisoning and membership inference attacks, thereby improving the security of FL in 5G networks.