We present a new image of the 5.5 GHz radio emission from the extended Chandra Deep Field South. Deep radio observations at 5.5 GHz were obtained in 2010 and presented in the first data release. A further 76 h of integration has since been obtained, nearly doubling the integration time. This paper presents a new analysis of all the data. The new image reaches 8.6 mu Jy rms, an improvement of about 40 per cent in sensitivity. We present a new catalogue of 5.5 GHz sources, identifying 212 source components, roughly 50 per cent more than were detected in the first data release. Source counts derived from this sample are consistent with those reported in the literature for S-5.5 GHz > 0.1 mJy but significantly lower than published values in the lowest flux density bins (S-5.5 GHz <0.1 mJy), where we have more detected sources and improved statistical reliability. The 5.5 GHz radio sources were matched to 1.4 GHz sources in the literature and we find a mean spectral index of -0.35 +/- 0.10 for S-5.5 GHz > 0.5 mJy, consistent with the flattening of the spectral index observed in 5 GHz sub-mJy samples. The median spectral index of the whole sample is alpha(med) =-0.58, indicating that these observations may be starting to probe the star-forming population. However, even at the faintest levels (0.05 <S-5.5 GHz <0.1 mJy), 39 per cent of the 5.5 GHz sources have flat or inverted radio spectra. Four flux density measurements from our data, across the full 4.5-6.5 GHz bandwidth, are combined with those from literature and we find 10 per cent of sources (S-5.5 GHz greater than or similar to 0.1 mJy) show significant curvature in their radio spectral energy distribution spanning 1.4-9 GHz.