The leap from 4G to 5G technology is set to revolutionize our digital lives with faster speeds, lower latency, and better connectivity. However, this advancement brings significant privacy concerns, particularly regarding location data. The 5G standard includes a Subscription Concealed Identifier (SUCI) to enhance privacy by hiding users' permanent identifiers. Yet, SUCI's optional nature and the need for SIM card updates hinder its widespread use. Additionally, 5G's advanced features like beamforming and network slicing, though useful for precision services, create new risks by enabling precise location tracking. This paper examines why SUCI alone cannot adequately protect location privacy in 5G networks. We analyze how 5G improvements impact privacy, reveal vulnerabilities in network slicing, and propose enhanced identity verification and security measures. Our study underscores the necessity for comprehensive privacy protections to mitigate the complex threats in the 5G era.