The fifth generation new radio (5G NR) technology is expected to fulfill reliable and accurate positioning requirements of industry use cases, such as autonomous robots, connected vehicles, and future factories. Starting from Third Generation Partnership Project (3GPP) Release-16, several enhanced positioning solutions are featured in the 5G standards, including the multi-cell round trip time (multi-RTT) method. This work presents a novel framework to estimate the round-trip time (RTT) between a user equipment (UE) and a base station (gNB) in 5G NR. Unlike the existing scheme in the standards, RTT can be estimated without the need to send timing measurements from both the gNB and UE to a central node. The proposed method relies on obtaining multiple coherent uplink wide-band channel measurements at the gNB by circumventing the timing advance control loops and the clock drift. The performance is evaluated through experiments leveraging a real world 5G testbed based on OpenAirInterface (OAI). Under a moderate system bandwidth of 40MHz, the experimental results show meter level range accuracy even in low signal-to-noise ratio (SNR) conditions.