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In this paper, the problem of content caching in 5G cellular networks relying on social-aware device-to-device communications (DTD) is investigated. Our focus is on how to efficiently select important users (IUs) and how to allocate content files to the storage of these selected IUs to form a distributed caching system. We aim at proposing a novel approach for minimizing the downloading latency and maximizing the social welfare simultaneously. In particular, we first model the problem of maximizing the social welfare as a many-to-one matching game based on the social property of mobile users. We study this game by exploiting users' social properties to generate the utility functions of the two-side players, i.e., content providers (CPs) and IUs. Then we model the problem of minimizing the downloading latency as a many-to-many matching problem. For solving these games, we design a many-to-one IU selection (MOIS) matching algorithm and a many-to-many file allocation (MMFA) matching algorithm, respectively. Simulation and analytical results show that the proposed mechanisms are stable, and are capable of offering a better performance than other benchmarks in terms of social welfare and network downloading latency.