An analysis of the 5 minute oscillation in the solar photosphere has been carried out using an inversion of the radiative transfer equation applied to a time-series of K I lambda 7699 line spectra with a 5" x 5" window at disk center. A thorough discussion of the inversion conditions, with special emphasis on the LTE approach and a careful error treatment, is offered. The inversion has been performed introducing fixed non-LTE departure coefficients taken from the literature. A sequence of instantaneous model atmospheres has been obtained, reliable from log tau ~= 0 to log tau ~= -3.5. From the temporal power spectra of line-of-sight velocity and temperature fluctuations, the amplitude and phase stratifications of the oscillations of these magnitudes have been obtained as functions of the optical depth. The amplitude accuracies are better than 4 m s-1 and 2 K in most of the photosphere. The increase of the velocity oscillation amplitude toward higher photospheric layers has been confirmed and quantified. Its phase angle remains constant through the photosphere, and significant power is obtained in temperature.