The bond dissociation energies (BDE) of most main-group elements have been accurately measured. However, the BDE values for heavy elements, particularly those from the fifth period (InI), are still missing or poorly validated. This study aims to identify the most accurate computational methods for calculating BDE values of compounds containing fifth-row elements, including In, Sn, Sb, Te, and I, with a focus on readily accessible methods in software packages. The investigation involved a benchmark study using density functional theory (DFT), in addition to the 2nd order Møller–Plesset perturbation theory (MP2) and the coupled cluster with single, double, and perturbative triple excitations CCSD(T). The DFT functionals used in the study include APFD, B3LYP, B3LYP-D3, B3P86, B97-D3, BHandH, HSEH1PBE, M06-2X, MN12-SX, MN15-L, and TPSSH. The functionals were carefully selected to cover some popular functionals as well as to cover all levels of the Jacob's ladder of DFT accuracy. The computed BDE values were compared with experimental values, and the results were filtered to remove any possible outliers. The statistical errors (MAPE, RMSE, and Pearson's) were then calculated and used to assess the performance of the methods.