We present an analysis of the diffuse emission at 5 GHz in the first quadrant of the Galactic plane using two months of preliminary intensity data taken with the C-Band All-Sky Survey (C-BASS) northern instrument at the Owens Valley Radio Observatory, California. Combining C-BASS maps with ancillary data to make temperature–temperature plots, we find synchrotron spectral indices of β = −2.65 ± 0.05 between 0.408 and 5 GHz and β = −2.72 ± 0.09 between 1.420 and 5 GHz for −10° < |b| < −4°, 20° < l < 40°. Through the subtraction of a radio recombination line free–free template, we determine the synchrotron spectral index in the Galactic plane (|b| < 4°) to be β = −2.56 ± 0.07 between 0.408 and 5 GHz, with a contribution of 53 ± 8 per cent from free–free emission at 5 GHz. These results are consistent with previous low-frequency measurements in the Galactic plane. By including C-BASS data in spectral fits, we demonstrate the presence of anomalous microwave emission (AME) associated with the H ii complexes W43, W44 and W47 near 30 GHz, at 4.4σ, 3.1σ and 2.5σ, respectively. The CORNISH (Co-Ordinated Radio ‘N’ Infrared Survey for High mass star formation) VLA 5-GHz source catalogue rules out the possibility that the excess emission detected around 30 GHz may be due to ultracompact H ii regions. Diffuse AME was also identified at a 4σ level within 30° < l < 40°, −2° < b < 2° between 5 and 22.8 GHz.