Geometries and energy separations of 32 low-lying electronic states of Rh-5 with different structures have been investigated. Complete active space multi-configuration self-consistent held method followed by large scale multireference singles + doubles configuration interaction computations that included up to 2.09 million configurations were used. Three nearly degenerate electronic states, namely, B-2(2)(C-2v) with a distorted trigonal bipyramid, (4)A(2)(C-2v) with a distorted trigonal bipyramid, and 4A,(C,,) with a distorted tetragonal geometry were found as candidates for the ground state of Rh-5. The calculated ionization potential from the ground state structure was found to be within the observed experimental range. The atomization and dissociation energies have also been computed and the results are compared with the smaller clusters.