Although neutral and ionic O4(0/-/+) species have been observed experimentally and considered for energetic materials, O4(2-) and O5(2-) dianions have not yet been explored. O4(2-) is valent isoelectronic to the well-known ClO3- and SO3(2-) anions, and O5(2-) is valent isoelectronic to ClO4- and SO4(2-). All are stable, common anions in solutions and inorganic salts. In this article, we explore the possibility of making covalently bound O4(2-) and O5(2-) species stabilized in the forms of M+O4(2-) and M+O5(2-) (M = Li, Na, K, Cs) in the gas phase. Laser vaporization experiments using M-containing targets and an O2-seeded carrier gas yielded very intense mass peaks corresponding to MO4- and MO5-. To elucidate the structure and bonding of the newly observed MO4- and MO5- species, we measured their photoelectron spectra and then compared them with ab initio calculations and the spectra of ClO3-, Na+SO3(2-), ClO4-, and Na+SO4(2-). Careful analyses of the experimental and ab initio results showed, however, that the observed species are of the forms, O2-M+O2- and O2-M+O3-. The more interesting M+O4(2-) and M+O5(2-) species were found to be higher-energy isomers, but they are true minima on the potential energy surfaces, which suggests that it might be possible to synthesize bulk materials containing covalently bound tetra- and pentatomic oxygen building blocks.