This paper proposes a physical-layer cell identity (PCID) detection method that uses joint estimation of the frequency offset and secondary synchronization signal (SSS) sequence for the 5G new radio (NR) initial access with beamforming transmission at a base station. Computer simulation results show that using the PCID detection method with the proposed joint estimation yields an almost identical PCID detection probability as the primary synchronization signal (PSS) detection probability at an average received signal-to-noise ratio (SNR) of higher than approximately -5dB suggesting that the residual frequency offset is compensated to a sufficiently low level for the SSS sequence estimation. It is also shown that the PCID detection method achieves a high PCID detection probability of greater than 90% and 50% at the carrier frequency of 30 and 50GHz, respectively, at the average received SNR of 0dB for the frequency stability of a user equipment oscillator of 3ppm.