The structural and electronic properties of the five isolated-pentagon fullerene isomers of C-78 were studied employing various quantum-chemistry methods ranging from the self-consistent Hartree-Fock method to the local-density-functional theory. Our results reveal that the energy ordering difference for the Hartree-Fock and local density functional calculations is intrinsic to the underlying approximation scheme, independent of the basis set used. Furthermore, the local-density function calculation results yield the same ordering for the total energy and the gap between highest occupied molecular orbital and lowest unoccupied molecular orbital for various basis sets and exchange functions, as well as a correlation between the averaged pentagon bond length and the gap between the highest occupied molecular orbital and the lowest unoccupied molecular orbital.