We present a table-top soft-x-ray spectrometer for the wavelength range λ = 1-5 nm based on a stable laser-driven x-ray source, making use of a gas-puff target. With this setup, optical light-pump/soft-x-ray probe near-edge x-ray absorption fine structure (NEXAFS) experiments with a temporal resolution of about 230 ps are feasible. Pump-probe NEXAFS measurements were carried out in the "water-window" region (2.28 nm-4.36 nm) on the manganite Pr(0.7)Ca(0.3)MnO(3), investigating diminutive changes of the oxygen K edge that derive from an optically induced phase transition. The results show the practicability of the table-top soft-x-ray spectrometer on demanding investigations so far exclusively conducted at synchrotron radiation sources.