Using the Hubble Space Telescope (HST) and the Large Binocular Telescope, we followed the evolution of the Type Ia supernova (SN Ia) 2011fe for an unprecedented 1840 days past B-band maximum light and over a factor of 7 million in flux. At 1840 days, the 4000-17000{AA} quasi-bolometric luminosity is just (420+/-20)L_{sun}_. By measuring the late-time quasi-bolometric light curve, we present the first confident detection of ^57^Co decay in a SN Ia light curve and estimate a mass ratio of log(^57^Co/^56^Co)=-1.59_-0.07_^+0.06^. We do not have a clean detection of ^55^Fe, but find a limit of ^55^Fe/^57^Co<0.22 with 99% confidence. These abundance ratios provide unique constraints on the progenitor system because the central density of the exploding white dwarf(s) dictates these nucleosynthetic yields. The observed ratios strongly prefer the lower central densities of double-degenerate models (^55^Fe/^57^Co=0.27) over the higher central densities of near-Chandrasekhar-mass single-degenerate models (^55^Fe/^57^Co=0.68). However, additional theoretical studies predicting isotopic yields from a broader range of progenitor systems are motivated by these unique observations. We will continue to observe SN 2011fe for another ~600 days with HST and possibly beyond.