Network slicing is a novel 5G paradigm that exploits the virtualization and softwarization of networks to create different logical network instances over a common network infrastructure. Each instance is tailored for specific Quality of Service (QoS) profiles so that network slicing can simultaneously support several services with diverse requirements. Network slicing can be applied at the Core Network or at the Radio Access Network (RAN). RAN slicing is particularly relevant to support latency-sensitive or time-critical applications since the RAN accounts for a significant part of the end-to-end transmission latency. In this context, this study proposes a novel latency-sensitive 5G RAN slicing solution. The proposal includes schemes to design slices and partition (or allocate) radio resources among slices. These schemes are designed with the objective to satisfy both the rate and latency demands of diverse applications. In particular, this study considers applications with deterministic aperiodic, deterministic periodic and non-deterministic traffic. The latency-sensitive 5G RAN slicing proposal is evaluated in Industry 4.0 scenarios where stringent and/or deterministic latency requirements are common. However, it can be evolved to support other verticals with latency-sensitive or time-critical applications.