With the great success of the second-generation wireless telephone technology and the third-generation mobile telecommunications technology, and the fast development of the fourth-generation mobile telecommunications technology, the phase of fifth-generation mobile networks or fifth-generation wireless systems (5G) is coming. In this article, we indicate the open research issues of 5G security and trust in the context of virtualized networking and software-defined networking. We further propose a framework of security and trust focusing on solving 5G network security issues. The proposed framework applies adaptive trust evaluation and management technologies and sustainable trusted computing technologies to ensure computing platform trust and achieve software-defined network security. It adopts cloud computing to securely deploy various trustworthy security services over the virtualized networks. We analyze that the framework can support and satisfy all security requirements specified in standardization. We also suggest future research work according to the proposed framework and discuss the advantages of our framework in terms of practical deployment. Copyright (C) 2015 John Wiley & Sons, Ltd.