The Internet of Things is a novel paradigm with access to wireless communication systems and artificial intelligence technologies, which is considered to be applicable to a variety of promising fields and applications. Meanwhile, the development of the fifth-generation cellular network technologies creates the possibility to deploy enormous sensors in the framework of the IoT and to process massive data, challenging the technologies of communications and data mining. In this article, we propose a novel paradigm, 5G Intelligent Internet of Things (5G I-IoT), to process big data intelligently and optimize communication channels. First, we articulate the concept of the 5G I-IoT and introduce three major components of the 5G I-IoT. Then we expound the interaction among these components and introduce the key methods and techniques based on our proposed paradigm, including big data mining, deep learning, and reinforcement learning. In addition, an experimental result evaluates the performance of 5G I-IoT, and the effective utilization of channels and QoS have been greatly improved. Finally, several application fields and open issues are discussed.