5G is destined to be supporting large deployment of Industrial IoT (IIoT) with the characteristics of ultra-high densification and low latency. 5G utilizes a more intelligent architecture, with Radio Access Networks (RANs) no longer constrained by base station proximity or proprietary infrastructure. The 3rd Generation Partnership Project (3GPP) covers telecommunication technologies including RAN, core transport networks and service capabilities. Open RAN Alliance (O-RAN) aims to define implementation and deployment architectures, focusing on open-source interfaces and functional units to further reduce the cost and complexity. O-RAN based 5G networks could use components from different hardware and software vendors, promoting vendor diversity, interchangeability and 5G supply chain resiliency. Both 3GPP and O-RAN 5G have to manage the security and privacy challenges that arose from the deployment. Many existing research studies have addressed the threats and vulnerabilities within each system. 5G also has the overwhelming challenges in compliance with privacy regulations and requirements which mandate the user identifiable information need to be protected. In this paper, we look into the 3GPP and O-RAN 5G security and privacy designs and the identified threats and vulnerabilities. We also discuss how to extend the Zero Trust Model to provide advanced protection over 5G air interfaces and network components.