Unmanned aerial vehicles, also called drones, are recently gaining increased research attention across various fields due to their flexibility and application potential. The steady increase in the number of amateur drones demands more stringent regulations on their allowed route, mass, and load. However, these regulations may be violated accidentally or deliberately. In these cases, spying with drones, transfer of dangerous payloads, or losing reliable drone control can represent a new hazard for people, governments, and business sector. The technologies to detect, track, and disarm possible aerial threats are therefore in prompt demand. To this end, ubiquitous cellular networks, and especially 5G infrastructures based on the use of millimeter-wave radio modules, may be efficiently leveraged to offer the much needed drone detection capabilities. In this work, we propose to exploit 5G millimeter-wave deployments to detect violating amateur drones. We argue that the prospective 5G infrastructure may provide all the necessary technology elements to support efficient detection of small-sized drones. We therefore outline a novel technology and system design perspective, including such considerations as the density of base stations, their directional antennas, and the available bandwidth, among others, as well as characterize their impact with our ray-based modeling methods.