We present lambda / DELTA lambda = 550 to 1200 near infrared H and K spectra for a magnitude limited sample of 79 asymptotic giant branch and cool supergiant stars in the central 5 pc (diameter) of the Galaxy. We use a set of similar spectra obtained for solar neighborhood stars with known \teff and \mbol that is in the same range as the Galactic center (GC) sample to derive \teff and \mbol for the GC sample. We then construct the Hertzsprung-Russell (HRD) diagram for the GC sample. Using an automated maximum likelihood routine, we derive a coarse star formation history of the GC. We find (1) roughly 75% of the stars formed in the central few pc are older than 5 Gyr; (2) the star formation rate (SFR) is variable over time, with a roughly 4 times higher star formation rate in the last 100 Myr compared to the average SFR; (3) our model can only match dynamical limits on the total mass of stars formed by limiting the IMF to masses above 0.7 Mo. This could be a signature of mass segregation or of the bias toward massive star formation from the unique star formation conditions in the GC; (4) blue supergiants account for 12 % of the total sample observed, and the ratio of red to blue supergiants is roughly 1.5; (5) models with isochrones with [Fe/H] = 0.0 over all ages fit the stars in our HRD better than models with lower [Fe/H] in the oldest age bins, consistent with the finding of Ramirez et al. (2000) that stars with ages between 10 Myr and 1 Gyr have solar [Fe/H].