Recent deep Chandra observations of nearby Compton-thick (CT) active galactic nuclei (AGNs) have produced surprising results, uncovering extended emission not only in soft X-rays but also in hard emission (>3 keV), challenging the long-held belief that the characteristic hard X-ray continuum and fluorescent Fe K lines are associated with the torus in the standard picture of AGNs. In this work, we present an analysis of our deep (∼261 ks) X-ray Chandra ACIS-S observations of NGC 5728, a nearby (z = 0.00932) CT AGN. We find that the diffuse emission is more extended at lower energies, in the bicone direction out to ∼2 kpc radially, but also significantly extended in the direction of the cross-cone, out to ∼1.4 kpc. Our results suggest that the ratio of detected photons in the cross-cone to the bicone region is ∼16%, below 3 keV, decreasing to 5% for energies 3–6 keV. The nuclear spectrum suggests a low-photoionization phase mixed with a more ionized gas component, while the bicone and cross-cone spectra are dominated by a mix of photoionization and shocked gas emission. A mixture of thermal and photoionization models used to fit the spectra indicates the presence of complex gas interactions, consistent with previous observations of other CT AGNs (e.g., ESO 428-G014).