We report on the host properties of five X-ray-luminous active galactic nuclei (AGN) identified at 3 < z < 5 in the first epoch of imaging from the Cosmic Evolution Early Release Science Survey. Each galaxy has been imaged with the JWST Near-Infrared Camera, which provides rest-frame optical morphologies at these redshifts. We also derive stellar masses and star formation rates for each host by fitting its spectral energy distribution using a combination of galaxy and AGN templates. We find that three of the AGN hosts have spheroidal morphologies, one is a bulge-dominated disk, and one is dominated by pointlike emission. None are found to show strong morphological disturbances that might indicate a recent interaction or merger event. When compared to a sample of mass-matched inactive galaxies, we find that the AGN hosts have morphologies that are less disturbed and more bulge-dominated. Notably, all four of the resolved hosts have rest-frame optical colors consistent with a quenched or poststarburst stellar population. The presence of AGN in passively evolving galaxies at z > 3 is significant because a rapid feedback mechanism is required in most semianalytic models and cosmological simulations to explain the growing population of massive quiescent galaxies observed at these redshifts. Our findings show that AGN can continue to inject energy into these systems after their star formation is curtailed, potentially heating their halos and preventing renewed star formation. Additional observations will be needed to determine what role this feedback may play in helping to quench these systems and/or maintain their quiescent state.