The forthcoming communication networks for public safety authorities rely on the fifth generation (5G) of mobile networking technologies. Police officers, paramedics, border guards, as well as fire and rescue personnel, will connect through commercial operator's access network and rapidly deployable tactical bubbles. This transition from closed and dedicated infrastructure to hybrid architecture will expand the threat surface and expose mission-critical applications and sensitive information to cyber and physical adversaries. We explore and survey security architecture and enablers for prioritized public safety communication in 5G networks. We identify security threat scenarios and analyze enabling vulnerabilities, threat actors, attacks vectors, as well as risk levels. Security enablers are surveyed for tactical access and core networks, commercial infrastructure, and mission-critical applications, starting from push-to-talk and group video communication and leading to situational-awareness and remote-controlled systems. Two solutions are trialed and described in more detail: remote attestation enhanced access control for constrained devices, and securing of satellite backhauls. We also discuss future research directions highlighting the need for enablers to automate security of rapid deployments, for military-grade cost-effective customizations of commercial network services to ensure robustness, and for hardening of various types of public safety equipment.