Since launch in 2008, the Fermi Gamma-ray Burst Monitor (GBM) has detected many hundreds of bursts from magnetar sources. While the vast majority of these bursts have been attributed to several known magnetars, there is also a small sample of magnetar-like bursts of unknown origin. Here, we present the Fermi/GBM magnetar catalog, providing the results of the temporal and spectral analyses of 440 magnetar bursts with high temporal and spectral resolution. This catalog covers the first five years of GBM magnetar observations, from 2008 July to 2013 June. We provide durations, spectral parameters for various models, fluences, and peak fluxes for all the bursts, as well as a detailed temporal analysis for SGR J1550-5418 bursts. Finally, we suggest that some of the bursts of unknown origin are associated with the newly discovered magnetar 3XMM J185246.6+0033.7.