This paper presents an analytical framework for clustered cooperative spectrum sensing (CSS) in dynamic 5G new radio (NR) vehicular networks, accounting for time-selective Nakagami- $m$ fading, mobility-induced decorrelation, and noisy reporting channels. We derive closed-form moments and detection probabilities for the $p$-norm detector under Jakes’ Doppler model, extending prior static analyses to realistic vehicular mobility. At the cluster head, we compare two fusion schemes: reliability weighting (based on long-term secondary user (SU) performance) and adaptive weighting (based on instantaneous statistics, with finite-sample variance derived via delta method). Results show that adaptive weighting outperforms the benchmark equal-weighting scheme by up to 5 dB in required signal-to-noise ratio (SNR) to achieve probability of detection at the fusion center $P_d^{\mathrm{F}\mathrm{C}}\ge 0.7$ under low-to-moderate SNR ( $<10$ dB) and high-mobility mmWave conditions (carrier frequency $f_c=28$ GHz, velocity $v\ge 110$ km/h), owing to its robustness to Doppler-induced channel de-correlation via self-normalised weight computation. Reliability weighting is superior at high SNR ( $\ge 10$ dB) and under low-mobility, near-AWGN conditions ( $f_c=3.5$ GHz, $m\ge 6$), where its lower-variance fixed-weight statistic yields more stable CFAR threshold calibration. Both proposed schemes consistently outperform the equal-weighting baselines across all three 5G NR configurations (3.5/28 GHz, 30/60/120 kHz sub-carrier spacing (SCS)) and vehicular speeds (70–150 km/h), providing mobility-aware design guidelines for next-generation cognitive radio systems.