Integrated Sensing and Communications (ISAC) is regarded as a key element of the beyond-fifth-generation (5G) and sixth-generation (6G) systems, raising the question of whether current 5G New Radio (NR) signal structures can meet the sensing accuracy requirements specified by the Third Generation Partnership Project (3GPP). This paper addresses this issue by analyzing the fundamental limits of range and velocity estimation through the Cramér-Rao lower bound (CRLB) for a monostatic unmanned aerial vehicle (UAV) sensing use case currently under consideration in the 3GPP standardization process. The study focuses on standardized signals and also evaluates the potential performance gains achievable with reference signals specifically designed for sensing purposes. The compact CRLB expressions derived in this work highlight the fundamental trade-offs between estimation accuracy and system parameters. The results further indicate that information from multiple slots must be exploited in the estimation process to attain the performance targets defined by the 3GPP. As a result, the 5G NR positioning reference signal (PRS), whose patterns may be suboptimal for velocity estimation when using single-slot resources, becomes suitable when multislot estimation is employed. Finally, we propose a two-step iterative range and radial-velocity estimator that attains the CRLB over a significantly wider range of distances than conventional maximum-likelihood (ML) estimators, for which the well-known threshold effect severely limits the distance range over which the accuracy requirements imposed by the 3GPP are satisfied.