The intrinsic radiative lifetimes of the $5d^{10}6s$ $^{2}text{S}_{1/2}$ and $5d^{9}6s^{2}$ $^{2}text{D}_{3/2}$ bound excited states in the platinum anion $text{Pt}^{-}$ have been studied at cryogenic temperatures at the Double ElectroStatic Ion Ring Experiment (DESIREE) facility at Stockholm University. The intrinsic lifetime of the higher-lying $5d^{10}6s$ $^{2}text{S}_{1/2}$ state was measurement to be 2.54$pm$0.10 s, while only a lifetime in the range of 50 - 200 ms could be estimated for the $5d^{9}6s^{2}$ $^{2}text{D}_{3/2}$ fine-structure level. The storage lifetime of the $text{Pt}^{-}$ ion beam was measured to be a little over 15 minutes at a ring temperature of 13 K. The present study reports the lifetime of an atomic negative ion in an excited bound state with an electron configuration different from that of the ground state.