We present the first results from the deep and wide 5 GHz radio observations of the Great Observatories Origins Deep Survey ( GOODS ) -North ( \sigma = 3.5 \mu Jy beam ^ { -1 } , synthesized beam size \theta = 1.47 \arcsec \times 1.42 \arcsec , and 52 sources over 109 arcmin ^ { 2 } ) and GOODS-South ( \sigma = 3.0 \mu Jy beam ^ { -1 } , \theta = 0.98 \arcsec \times 0.45 \arcsec , and 88 sources over 190 arcmin ^ { 2 } ) fields using the Karl G. Jansky Very Large Array .
We derive radio spectral indices \alpha between 1.4 and 5 GHz using the beam-matched images and show that the overall spectral index distribution is broad even when the measured noise and flux bias are considered .
We also find a clustering of faint radio sources around \alpha = 0.8 , but only within S _ { 5 GHz } < 150 \mu Jy .
We demonstrate that the correct radio spectral index is important for deriving accurate rest frame radio power and analyzing the radio-FIR correlation , and adopting a single value of \alpha = 0.8 leads to a significant scatter and a strong bias in the analysis of the radio-FIR correlation , resulting from the broad and asymmetric spectral index distribution .
When characterized by specific star formation rates , the starburst population ( 58 % ) dominates the 5 GHz radio source population , and the quiescent galaxy population ( 30 % ) follows a distinct trend in spectral index distribution and the radio-FIR correlation .
Lastly , we offer suggestions on sensitivity and angular resolution for future ultra-deep surveys designed to trace the cosmic history of star formation and AGN activity using radio continuum as a probe .