5G will provide broadband access everywhere, entertain higher user mobility, and enable connectivity of massive number of devices (e.g. Internet of Things (IoT)) in an ultrareliable and affordable way. The main technological enablers such as cloud computing, Software Defined Networking (SDN) and Network Function Virtualization (NFV) are maturing towards their use in 5G. However, there are pressing security challenges in these technologies besides the growing concerns for user privacy. In this paper, we provide an overview of the security challenges in these technologies and the issues of privacy in 5G. Furthermore, we present security solutions to these challenges and future directions for secure 5G systems.