The possible existence of the CF5-, CCl5-, SiF5-, SiCl5-, GeF5-, and GeCl5- anions has been investigated using ab initio methods. The species containing Si and Ge as central atoms were found to adopt the D-3h-symmetry trigonal bipyrarnidal equilibrium structures whose thermodynamic stabilities were confirmed by examining the most probable fragmentation channels. The ab initio re-examination of the electronic stabilities of the SiF5-, SiCl5-, GeF5-, and GeCl5- anions [using the OVGF(full) method with the 6-311+G(3df) basis set] led to the very large vertical electron detachment (VDE) energies of 9.316 eV (SiF5-) and 9.742 eV (GeF5-), whereas smaller VDEs of 6.196 and 6.452 eV were predicted for the SiCl5- and GeCl5- species, respectively. By contrast, the high-symmetry and structurally compact anionic CF5- and CCl5- systems cannot exist due to the strongly repulsive potential predicted for the X- (F- or Cl-) approachingthe CX4 (CF4 or CCl4). The formation of weakly bound CX4 center dot center dot center dot X- (CF4 center dot center dot center dot F- and CCl4 center dot center dot center dot Cl-) anionic complexes (consisting of pseudotetrahedral neutral CX4 with the weakly tethered X-) might be expected at low temperatures (approaching 0 K), whereas neither CX5- (CF5-, CCl5-) systems nor CX4 center dot center dot center dot X- (CF4 center dot center dot center dot F- and CCl4 center dot center dot center dot C-) complexes can exist in the elevated temperatures (above 0K) due to their susceptibility to the fragmentation (leading to the X- loss).