To enable widespread use of Integrated Sensing and Communication (ISAC) in future communication systems, an important requirement is the ease of integration. A possible way to achieve this is to use existing communication reference signals for sensing, such as the 5G Positioning Reference Signal (PRS). Existing works have demonstrated promising results by using the PRS with classical signal processing techniques. However, this approach suffers from a loss of SNR due to the sparse resource allocation. In this work, we improve upon existing results by combining the 5G PRS with compressed sensing methods. We demonstrate that our method achieves better noise robustness compared to the existing works and has superresolution properties, making it an ideal choice for range-Doppler map generation and target detection even in noisy environments.