This paper explores the integration of Time-Sensitive Networking (TSN) with 5G cellular networks to support high-bandwidth and low-latency end-to-end communication in networked embedded systems. Integrating TSN with 5G has the potential to support predictable and deterministic end-to-end communication, as well as to significantly enhance scalability, particularly in industrial automation, by providing flexibility, efficiency, and responsiveness. To ensure smooth integration while preserving TSN's Quality of Service (QoS) requirements, effective traffic translation and forwarding within the network are crucial. In this regard, this paper addresses key challenges related to traffic translation, QoS implementation, and latency in both TSN and private 5G networks on a realistic scenario. Through experiments, measurements, and evaluation, this paper thoroughly assesses latency and network capabilities in the integrated networks. Understanding these metrics is essential for devising effective integration strategies. Our findings indicate that it is possible to achieve latencies under 20 ms in an integrated TSN-5G network, given our specific configuration of a private 5G setup with a channel bandwidth of 40 MHz. We also identify an urgent need for the implementation of a proper QoS mechanism in the Open Air Interface software to enable the prioritization of high-critical data transmission.