Segmented all-electron basis set of triple zeta valence quality plus polarization functions (TZP) for the elements of the fifth row to be used together with the zero-order regular approximation (ZORA) was carefully constructed. To correctly describe electrons distant from atomic nuclei, the basis set was augmented with diffuse functions giving rise to a set designated as ATZP-ZORA. At the ZORA-B3LYP theory level, these sets were used to calculate ionization energies and mean dipole polarizabilities of some atoms and bond lengths, dissociation energies, and harmonic vibrational frequencies of diatomic molecules. Then, these results were compared with theoretical and experimental data found in the literature. Even considering that our sets are relatively compact, they are sufficiently accurate and reliable to perform property calculations involving simultaneously electrons from the inner and outer shells. An evaluation of the performances of the ZORA and second-order Douglas-Kroll-Hess Hamiltonians was carried out and the results are here discussed.