Providing ubiquitous connectivity to diverse device types is the key challenge for 5G and beyond 5G (B5G). Unmanned aerial vehicles (UAVs) are expected to be an important component of the upcoming wireless networks that can potentially facilitate wireless broadcast and support high rate transmissions. Compared to the communications with fixed infrastructure, UAV has salient attributes, such as flexible deployment, strong line-of-sight connection links, and additional design degrees of freedom with the controlled mobility. In this paper, a comprehensive survey on UAV communication toward 5G/B5G wireless networks is presented. We first briefly introduce essential background and the space-air-ground integrated networks, as well as discuss related research challenges faced by the emerging integrated network architecture. We then provide an exhaustive review of various 5G techniques based on UAV platforms, which we categorize by different domains, including physical layer, network layer, and joint communication, computing, and caching. In addition, a great number of open research problems are outlined and identified as possible future research directions.