The UF(5)(-) and UF(6)(-) anions are produced using electrospray ionization and investigated by photoelectron spectroscopy and relativistic quantum chemistry. An extensive vibrational progression is observed in the spectra of UF(5)(-), indicating significant geometry changes between the anion and neutral ground state. Franck-Condon factor simulations of the observed vibrational progression yield an adiabatic electron detachment energy of 3.82 ± 0.05 eV for UF(5)(-). Relativistic quantum calculations using density functional and ab initio theories are performed on UF(5)(-) and UF(6)(-) and their neutrals. The ground states of UF(5)(-) and UF(5) are found to have C(4v) symmetry, but with a large U-F bond length change. The ground state of UF(5)(-) is a triplet state ((3)B(2)) with the two 5f electrons occupying a 5f(z3)-based 8a(1) highest occupied molecular orbital (HOMO) and the 5f(xyz)-based 2b(2) HOMO-1 orbital. The detachment cross section from the 5f(xyz) orbital is observed to be extremely small and the detachment transition from the 2b(2) orbital is more than ten times weaker than that from the 8a(1) orbital at the photon energies available. The UF(6)(-) anion is found to be octahedral, similar to neutral UF(6) with the extra electron occupying the 5f(xyz)-based a(2u) orbital. Surprisingly, no photoelectron spectrum could be observed for UF(6)(-) due to the extremely low detachment cross section from the 5f(xyz)-based HOMO of UF(6)(-).