This last decade, the amount of data exchanged in the Internet increased by over a staggering factor of 100, and is expected to exceed well over the 500 exabytes by 2020. This phenomenon is mainly due to the evolution of high speed broadband Internet and, more specifically, the popularization and wide spread use of smartphones and associated accessible data plans. Although 4G with its long-term evolution (LTE) technology is seen as a mature technology, there is continual improvement to its radio technology and architecture such as in the scope of the LTE Advanced standard, a major enhancement of LTE. But for the long run, the next generation of telecommunication (5G) is considered and is gaining considerable momentum from both industry and researchers. In addition, with the deployment of the Internet of Things (IoT) applications, smart cities, vehicular networks, e-health systems, and Industry 4.0, a new plethora of 5G services has emerged with very diverging and technologically challenging design requirements. These include: high mobile data volume per area, high number of devices connected per area, high data rates, longer battery life for low-power devices, and reduced end-to-end latency. Several technologies are being developed to meet these new requirements. Among these we list ultra-densification, millimeter Wave usage, antennas with massive multiple-input multiple-output (MIMO), antenna beamforming to increase spacial diversity, edge/fog computing, among others. Each of these technologies brings its own design issues and challenges. For instance, ultra-densification and MIMO will increase the complexity to estimate channel condition and traditional channel state information (CSI) estimation techniques are no longer suitable due to the complexity of the new scenarios. As a result, new approaches to evaluate network condition such as by continuously collecting and monitoring key performance indicators become necessary. Timely decisions are needed to ensure the correct operation of such network. In this context, deep learning (DL) models could be seen as one of the main tools that can be used to process monitoring data and automate decisions. As these models are able to extract relevant features from raw data (images, texts, and other types of unstructured data), the integration between 5G and DL looks promising and one that requires exploring. As main contributions, this paper presents a systematic review about how DL is being applied to solve some 5G issues. We examine data from the last decade and the works that addressed diverse 5G problems, such as physical medium state estimation, network traffic prediction, user device location prediction, self network management, among others. We also discuss the main research challenges when using DL models in 5G scenarios and identify several issues that deserve further consideration.