  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 hours 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 microJy rms,
an improvement of about 40% in sensitivity. We present a new catalogue of 5.5
GHz sources, identifying 212 source components, roughly 50% 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_{5.5GHz} > 0.1 mJy but
significantly lower than published values in the lowest flux density bins
(S_{5.5GHz} < 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_{5.5GHz} > 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_{5.5GHz} < 0.1 mJy), 39% of the 5.5 GHz sources have flat or
inverted radio spectra. Four flux density measurements from our data, across
the full 4.5 to 6.5 GHz bandwidth, are combined with those from literature and
we find 10% of sources (S_{5.5GHz} >~ 0.1 mJy) show significant curvature in
their radio spectral energy distribution spanning 1.4 to 9 GHz.
