Millimetre-wave communication (licensed or unlicensed) is envisaged to be an important part of the fifth generation (5G) multi-RAT ecosystem. In this paper, we consider the spectrum bands shared by 5G cellular base stations and some existing networks, such as WiGig. Sharing the same band among such multiple radio access technologies (RATs) is very challenging due to the lack of centralized coordination and demands novel and efficient interference mitigation and coexistence mechanisms to reduce the mutual interference. To address this important challenge, we propose in this paper a novel multi-RAT coexistence mechanism where neighbouring 5G and WiGig base stations, each serving their own associated UEs, schedule their beam configurations in a distributed manner such that their own utility function, e.g. spectral efficiency, is maximized. We formulate the problem as a combinatorial optimization problem and show via simulations that our proposed distributed algorithms yield a comparable spectral efficiency for the entire networks as that using an exhaustive search, which requires global coordination among coexisting RATs and also has a much higher algorithmic complexity.