Optimized geometries and C-13 NMR chemical shifts of all the isolated-pentagon-rule (TPR) isomers of fullerenes C-60, C-70, C-72, C-74, C-76, and C-78, except C-76:2, have been calculated by density functional theory (B31YP/6-31G*). C60 has the highest value of total energy per atom. The total energy per atom of other fullerenes decreases when the size of fullerene increases. The unobserved C-72 is found to have higher total energy per atom while the also unobserved fullerenes C-74, C-78:4, and C-78:5 have similar values of total energy per atom compared to those already observed. The general patterns of the calculated C-13 NMR spectra give good agreement with the experimental patterns. Peaks above 140 ppm agree better with experiment while chemical shifts below 140 ppm are generally overestimated by 1-2 ppm. Local geometry is shown to be determined largely by the connectivity and have some effect on chemical shifts although no direct relationship between the pi-orbital axis vector (POAV) angles and chemical shifts is apparent.