Mobile cellular networks are becoming increasingly complex to manage while classical deployment/optimization techniques and current solutions (i.e., cell densification, acquiring more spectrum, etc.) are cost-ineffective and thus seen as stopgaps. This calls for development of novel approaches that leverage recent advances in storage/memory, context-awareness, edge/cloud computing, and falls into framework of big data. However, the big data by itself is yet another complex phenomena to handle and comes with its notorious $4$V: velocity, voracity, volume and variety. In this work, we address these issues in optimization of $5G$ wireless networks via the notion of proactive caching at the base stations. In particular, we investigate the gains of proactive caching in terms of backhaul offloadings and request satisfactions, while tackling the large-amount of available data for content popularity estimation. In order to estimate the content popularity, we first collect users' mobile traffic data from a Turkish telecom operator from several base stations in hours of time interval. Then, an analysis is carried out locally on a big data platform and the gains of proactive caching at the base stations are investigated via numerical simulations. It turns out that several gains are possible depending on the level of available information and storage size. For instance, with $10\%$ of content ratings and $15.4$ Gbyte of storage size ($87\%$ of total catalog size), proactive caching achieves $100\%$ of request satisfaction and offloads $98\%$ of the backhaul when considering $16$ base stations.