The fifth-generation (5G) radio networks will support ultra-reliable low-latency communications (URLLC). In the uplink, the latency can be reduced by removing the time-consuming and error-prone scheduling procedure and, instead, using the grant-free (GF) transmissions. Reaching the strict URLLC reliability requirements with GF transmissions is, however, particularly challenging due to the wireless channel uncertainties and interference from other URLLC devices. As a consequence, the supported URLLC capacity and, hence, the spectral efficiency are typically low. Multi-cell reception, i.e., joint reception and combining by multiple base-stations (BS), is a technique known from long-term evolution (LTE), with the potential to greatly enhance the reliability. This paper proposes the use of multi-cell reception to increase the URLLC spectral efficiency while satisfying the strict requirements using GF transmissions in a 5G new radio (NR) scenario. We evaluate the achievable URLLC capacity for an elaborate multi-cell reception parameter space and multi-cell combining techniques. In addition, we demonstrate that rethinking of the radio resource management (RRM) in the presence of multi-cell reception is needed to unleash the full potential of multi-cell reception in the context of UL GF URLLC. It is observed that multi-cell reception, compared to a single-cell reception, can provide URLLC capacity gains from 205% to 440% when the BSs are equipped with two receive antennas and 53% to 22% when BSs are equipped with four receive antennas, depending on whether the retransmissions are enabled.