Star forming galaxies are thought to dominate the sub-mJy radio population , but recent work has shown that low luminosity AGN can still make a significant contribution to the faint radio source population . Spectral indices are an important tool for understanding the emission mechanism of the faint radio sources . We have observed the extended Chandra Deep Field South at 5.5 GHz using a mosaic of 42 pointings with the Australia Telescope Compact Array ( ATCA ) . Our image reaches an almost uniform sensitivity of \sim 12 \mu Jy rms over 0.25 deg ^ { 2 } with a restoring beam of 4.9 \times 2.0 arcsec , making it one of the deepest 6cm surveys to date . We present the 5.5 GHz catalogue and source counts from this field . We take advantage of the large amounts of ancillary data in this field to study the 1.4 to 5.5 GHz spectral indices of the sub-mJy population . For the full 5.5 GHz selected sample we find a flat median spectral index , \alpha _ { med } = -0.40 , which is consistent with previous results . However , the spectral index appears to steepen at the faintest flux density levels ( S _ { 5.5 GHz } < 0.1 mJy ) , where \alpha _ { med } = -0.68 . We performed stacking analysis of the faint 1.4 GHz selected sample ( 40 < S _ { 1.4 GHz } < 200 \mu Jy ) and also find a steep average spectral index , \alpha = -0.8 , consistent with synchrotron emission . We find a weak trend of steepening spectral index with redshift . Several young AGN candidates are identified using spectral indices , suggesting Gigahertz Peaked Spectrum ( GPS ) sources are as common in the mJy population as they are at Jy levels .