The energy levels of the n=5 complex configuration 5s2, 5s5p, 5s5d and 5p2 were computed for Cd Ⅰ isoelectronic sequence ions from I Ⅵ to Sm ⅩⅤ by Hartree-Fock with relativistic corrections (HFR) method. By analyzing the variation of difference ΔE between energy levels calculated by HFR method and the experimental values with Zc along this isoelectronic sequence, the authors put forward a new fitting formula for generalized-least-square-fit (LSF) calculation. Using this formula and the FORTRAN programme designed by us, the energy levels of configurations mentioned above were calculated. The unknown energy levels of configuration 5s2, 5s5p, 5s5d and 5p2 for ions from Nd -Sm ⅩⅤ were predicted by extrapolation (or interpolation). Also, the wavelengths and HFR probabilities of transition 5s2—5s5p, 5s5p—5p2 and 5s5p—5s5d were computed. The calculated energy levels and wavelength results are in good agreement with corresponding experimental data reported in the references.