The first theoretical investigation on the mechanism for ligand substitution in five-coordinate square pyramidal oxorhenium dithiolate complexes, CH3ReO(SCH2C6H4S)-X, has been carried out with the Perdew-Burke-Ernzerhof density functional and the Stuttgart relativistic effective-core-potential basis sets. In the mechanism proposed in the experimental kinetic studies, the entering ligand Y attacks the vacant lower axial coordinate site trans to O, and the resulting six-coordinate intermediate rearranges through a turnstile twist (a trigonal prismatic intermediate or transition state) or pentagonal pyramid to allow the leaving ligand X to exit from the same site. These workers proposed this rearrangement to avoid a violation of microscopic reversibility. The computed energy barriers in this reaction pathway show that the turnstile or pentagonal pyramidal transition states are too high in energy to make this pathway accessible. Although the vacant lower axial site in the rhenium complex is the site most easily attacked by Y, transition states for X leaving from the site cis to the attack have quite low energy barriers. Although this direct-exchange mechanism was thought to lead to a violation of microscopic reversibility, we show that these direct-exchange pathways provide low-energy routes for ligand exchange and clarify this apparent violation of microscopic reversibility. Furthermore, computed results of different entering and leaving ligand pairs are analyzed for their effect on the choice of reaction pathways. In the direct-exchange mechanism, the replacement of 4-Bu-t-pyridine by PPhMe2 is monophasic without an intermediate, but the replacement of PPh3 by PPhMe2 is biphasic (proceeds by a two-stage pathway) and generates the observed intermediate, an isomer of product. These predictions are completely consistent with the observed experimental phenomena. The accuracy of the particular functional/basis set used for the study is compared to 10 functionals in 19 basis sets and to large basis set coupled cluster calculations on model systems.