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A<sc>bstract</sc> We extend the Effective Field Theory of Heavy Dark Matter to arbitrary odd representations of SU(2) and incorporate the effects of bound states. This formalism is then deployed to compute the gamma-ray spectrum for a5of SU(2): quintuplet dark matter. Except at isolated values of the quintuplet mass, the bound state contribution to hard photons with energy near the dark-matter mass is at the level of a few percent compared to that from direct annihilation. Further, compared to smaller representations, such as the triplet wino, the quintuplet can exhibit a strong variation in the shape of the spectrum as a function of mass. Using our results, we forecast the fate of the thermal quintuplet, which has a mass of ~13.6 TeV. We find that existing H.E.S.S. data should be able to significantly test the scenario, however, the final word on this canonical model of minimal dark matter will likely be left to the Cherenkov Telescope Array (CTA).