We have carried out a spectroscopic study of asteroid 65 Cybele in the 2 - 4 μm and 5 - 14 μm regions, using NASA's IRTF and Spitzer Space Telescope, respectively. We compare these spectra with those of Trojan asteroids and asteroid 24 Themis. Our target is the largest member of the Cybele population; these asteroids represent a transition group between primitive inner-main belt asteroids and Trojans, and may provide clues to the origin of the asteroid belt and the solar system. Our 2 - 4 μm spectrum shows a clear absorption band centered at 3.1 μm, similar to that in the spectrum of 24 Themis (Campins et al. 2010, Rivkin & Emery 2010), which can be modeled using water-ice. Absorption bands in 65 Cybele's 3.2 - 3.6 μm region also suggest the presence of complex organic solids. No hydrated silicates are detected. We fit the 5 - 14 μm continuum using the NEATM (Harris 1998) and derived a diameter D = 290 ± 5 km (consistent with Müller and Bloemmaert 2004), beaming parameter η = 0.967 ± 0.014, and albedo pV = 0.05 ± 0.01. Once the continuum has been divided out, the 5 - 14 μm emissivity spectrum clearly exhibits an emission plateau at about 9 - 12 μm with a spectral contrast of about 5%. A similar feature is seen in the spectra of Trojan asteroids and may be due to fine-grained silicates imbedded in a transparent matrix, or to a very under-dense surface structure (Emery et al. 2006). We conclude that 65 Cybele is covered by fine anhydrous silicate grains, with a small amount of water-ice and complex organic solids. This is similar to comets where non-equilibrium phases coexist, e.g. water-ice and anhydrous silicates; thus we conclude that this is a very primitive object.