We present 5 GHz e-MERLIN observations of the GOODS-N region at sub-arcsec resolution (0.2--0.5 arcsec). These data form part of the early commissioning observations for the e-MERLIN interferometer and a pilot for the e-MERLIN legacy program eMERGE. A total of 17 sources were detected with S/N>3. These observations provide unique information on the radio source morphology at sub-arcsec scales. For twelve of these sources, deeper 1.4 GHz MERLIN+VLA observations at the same spatial resolution are available, allowing radio spectral indices to be derived for ten sources on sub-arcsec angular scales. Via analysis of the spectral indices and radio morphologies, these sources have been identified as AGN cores in moderate-to-high redshift (1<z<4) galaxies. These results have provided AGN (or AGN candidate) classification for six previously unclassified sources and confirmed the AGN nature of the rest of the sample. Ultimately the eMERGE project will image the GOODS-N region at 1.4 and 5 GHz with higher resolution (about 50 mas at 5 GHz) and down to sub-microJy sensitivities. The unique combination of sensitivity and spatial resolution will be exploited to study star formation and AGN activity in distant galaxies.