Industrial IoT has special communication requirements, including high reliability, low latency, flexibility, and security. These are instinctively provided by the 5G mobile technology, making it a successful candidate for supporting Industrial IoT (IIoT) scenarios. The aim of this paper is to identify current research challenges and solutions in relation to 5G-enabled Industrial IoT, based on the initial requirements and promises of both domains. The methodology of the paper follows the steps of surveying state-of-the art, comparing results to identify further challenges, and drawing conclusions as lessons learned for each research domain. These areas include IIoT applications and their requirements; mobile edge cloud; back-end performance tuning; network function virtualization; and security, blockchains for IIoT, Artificial Intelligence support for 5G, and private campus networks. Beside surveying the current challenges and solutions, the paper aims to provide meaningful comparisons for each of these areas (in relation to 5G-enabled IIoT) to draw conclusions on current research gaps.