Integrated sensing and communication (ISAC) is a promising technology to simultaneously provide high performance wireless communication and radar sensing services in future networks. In this paper, we propose the concept of integrated super-resolution sensing and communication (ISSAC), which uses super-resolution algorithms in ISAC systems to achieve extreme sensing performance for those critical parameters, such as delay, Doppler, and angle of the sensing targets. Based on practical fifth generation (5G) New Radio (NR) wave forms, the signal processing techniques of ISSAC are investigated and prototyping experiments are performed to verify the achievable performance. To this end, we first study the effect of uneven cyclic prefix (CP) lengths of 5G NR orthogonal frequency division multiplexing (OFDM) waveforms on various sensing algorithms. Specifically, the performance of the standard Periodogram based radar processing method, together with the two classical super resolution algorithms, namely, MUltiple SIgnal Classification (MUSIC) and Estimation of Signal Parameter via Rotational Invariance Techniques (ESPRIT) are analyzed in terms of the delay and Doppler estimation. To resolve the uneven CP issue, a new structure of steering vector for MUSIC and a new selection of submatrices for ESPRIT are proposed. Furthermore, an ISSAC experimental platform is setup to validate the theoretical analysis, and the experimental results show that the performance degradation caused by unequal CP length is insignificant and high-resolution delay and Doppler estimation of the target can be achieved with 5G NR waveforms.