The development of the fifth generation network (5G) enabled the connection of almost all aspects of life through a network characterised by a higher speed of data transfer, low latency and better connectivity in all parts of the world. The forthcoming fifth generation is an increasingly common topic in society which will soon become reality. The connection of a large number of devices in a network named the Internet of things will be enabled, but it will also have numerous other applications in smart cities and autonomous vehicles. The set of security threats in the 5G network increased enormously due to the proportional rise in the types of services and number of devices offering them. Therefore, security solutions, if not yet developed, have to be conceived so as to be able to deal with the various threats of different services, new technologies and the elevated number of information a user obtains through an accessible network. The topic of this paper relates to the security aspects of the 5G network. The security vulnerabilities of the 5G network infrastructure have been described, as well as the threats to the new technological concepts, solutions to those threats and guidelines for the solution of such security challenges in the future.