We exploit the new 7 Ms Chandra observations in the CDF-S, the deepest X-ray survey to date, coupled with CANDELS/GOODS- S data, to measure the total X-ray emission arising from ~2000 galaxies at 3.5 < z < 6.5. This aim is achieved by stacking the Chandra data at the positions of optically selected galaxies, reaching effective exposure times of >=10^9 s. We detect X-ray emission from z ‚ào 4 galaxies at 3 ‚àí 5sigma, while no significant signal is detected from galaxies at higher redshifts. The stacking results are used to estimate the black hole accretion rate density (BHAD) and star -formation rate density (SFRD) at high redshift, assuming a range of prescriptions for X-ray emission due to X-ray binaries. We find that X-ray emission from our sample is likely dominated by processes related to star formation. Our results show that low-rate mass accretion onto SMBHs in individually X-ray-undetected galaxies is negligible, compared with the BHAD measured for samples of X-ray detected AGN, for cosmic SMBH mass assembly at high redshift. We also place, for the first time, constraints on the faint-end of the AGN X- ray luminosity function (logLX ‚ào 42) at z > 4, with evidence for fairly flat slopes.