Global health challenges and the proliferation of mobile technologies have been key in the adoption of mHealth for provision of low-cost and equitable healthcare. Evolution of mobile networks to 5G is expected to revolutionise healthcare service delivery due to the stringent performance requirements imposed on 5G. However, because of the open nature of 5G systems, securing patient health information has been identified as a significant barrier to the full adoption of mHealth. In this paper, we propose a security architecture for an mHealth system based on a review of standard principles and guidelines for designing 5G security systems. We present a structured approach for developing and implementing an end-to-end 5G mHealth security system. We propose a security architecture that can be realised using keyless signature infrastructure blockchain, X-tee technology to secure the communication system including hospital and third-party health data networks, physical layer security for securing the wireless interface in access networks, physical unclonable functions, and a trusted execution environment for securing end-user devices. We propose the adoption of network slicing for isolating health systems from other 5G industry verticals. We define system domains that are used to identify security threats and propose mechanisms to mitigate these threats.