Communication and video capture from unmanned aerial vehicles (UAVs) offer significant potential for assisting first responders in remote public safety settings. In such uses, millimeter wave (mmWave) wireless links can provide high throughput and low latency connectivity between the UAV and a remote command center. However, maintaining reliable aerial communication in the mmWave bands is challenging due to the need to support high speed beam tracking and overcome blockage. This paper provides a simulation study aimed at assessing the feasibility of public safety UAV connectivity through a 5G link at 28 GHz. Real flight motion traces are captured during maneuvers similar to those expected in public safety settings. The motions traces are then incorporated into a detailed mmWave network simulator that models the channel, blockage, beamforming and full 3GPP protocol stack. We show that 5G mmWave communications can deliver throughput up to 1 Gbps with consistent sub ms latency when the base station is located near the mission area, enabling remote offloading of the UAV control and perception algorithms.