The next mobile generation, 5G, is expected to bring an enormous amount of new services and increased user experience. However adequate protection mechanisms for data and user privacy are required as this new technology will play a crucial role in society by connecting vertical industries, such as smart-grids, e-health, finance, transport and manufacturing. In this paper, we identify the most important privacy issues caused by the new technologies planned to use in 5G. Then, we discuss the objectives for privacy protection in 5G and correlate the identified issues with these objectives. Finally, we highlight how these objectives can be met by both a regulatory and technological approach. To this end, several privacy preserving technological solutions are presented for 5G networks.