The development of 5G terrestrial mobile communications technology has been a driving force for revolutionizing satellite mobile communications. Satellite mobile communications, which carry many unique features, such as large coverage and support for reliable emergency communications, should satisfy the requirements for convergence between terrestrial mobile communications and satellite mobile communications for future broadband hybrid S-T communications. On the other hand, CR is an attractive technique to support dynamic single-user or multi-user access in hybrid S-T communications. This article first discusses several key issues in applying cognitive radio to future broadband satellite communications toward 5G. Then we present an overview of future broadband hybrid S-T communications systems, followed by an introduction to a typical application scenario of futuristic CR-broadband hybrid S-T communication systems toward 5G. Moreover, we propose a space segment design based on a spectrum-sensing-based cooperative framework, in consideration of the presence of MUs. An experiment platform for the proposed CR-based hybrid S-T communications system is also demonstrated.