We experimentally demonstrate the performance gains achieved by an in-house built reconfigurable intelligent surface (RIS) integrated with a real-time 5G new radio (NR) system implemented using the OpenAirInterface (OAI) framework. We first quantify the gain in throughput achievable by integrating an RIS with a 5G system. Next, we show that randomly setting the RIS phase configuration and leveraging the inherent proportional fair (PF) scheduling mechanism of 5G NR can yield near-optimal throughput, provided the throughput averaging window of the PF scheduler is chosen judiciously. This occurs because, in each time slot, the PF scheduler naturally prioritizes data transmission to the user equipment (UE) that experiences the best channel conditions, namely, the UE to which the randomly configured RIS is aligned. Subsequently, we experimentally evaluate key performance metrics, including the reference signal received power (RSRP), block error rate (BLER), modulation and coding scheme (MCS) index, and throughput, under random RIS configurations. These results confirm that even a randomly configured RIS with negligible overhead can deliver performance comparable to optimized RIS designs, in real-world 5G NR wireless communication systems.