We search for high-redshift (z>4.5) X-ray AGNs in the deep central (off-axis angle <5.7) region of the 7 Ms Chandra Deep Field-South X-ray image. We compile an initial candidate sample from direct X-ray detections. We then probe more deeply in the X-ray data by using pre-selected samples with high spatial resolution NIR/MIR (HST 1.6 micron and Spitzer 4.5 micron) and submillimeter (ALMA 850 micron) observations. The combination of the NIR/MIR and submillimeter pre-selections allows us to find X-ray sources with a wide range of dust properties and spectral energy distributions (SEDs). We use the SEDs from the optical to the submillimeter to determine if previous photometric redshifts were plausible. Only five possible z>5 X-ray AGNs are found, all of which might also lie at lower redshifts. If they do lie at high redshifts, then two are Compton-thick AGNs, and three are ALMA 850 micron sources. We find that (i) the number density of X-ray AGNs is dropping rapidly at high redshifts, (ii) the detected AGNs do not contribute significantly to the photoionization at z>5, and (iii) the measured X-ray light density over z=5-10 implies a very low black hole accretion density with very little growth in the black hole mass density in this redshift range.