While the 1,5-sigmatropic hydrogen shift in cyclopentadiene is generally thought to be a unimolecular pericyclic reaction, Yamabe proposed a more complex bimolecular mechanism proceeding through the exo dimer of cyclopentadiene. DFT computations by Yamabe were claimed to show that the bimolecular mechanism was kinetically more favorable than the unimolecular mechanism. Reinvestigation of the unimolecular concerted mechanism and Yamabe's bimolecular mechanism with ωB97X-D and DLPNO-CCSD(T) calculations demonstrates a 25 kcal/mol preference for the unimolecular mechanism relative to the bimolecular mechanism. While Yamabe's calculations were performed with the less accurate B3LYP functional, the incorrect conclusion was the result of a different error discovered here. We have also computed corrections for tunneling that result in computed activation barriers within 1.5 kcal/mol of the experimental values.