We present deep spectroscopy from Keck/DEIMOS (DEep Imaging Multi-Object Spectrograph) of Andromeda I, III, V, VII, and X, all of which are dwarf spheroidal satellites (dSphs) of M31. The sample includes 256 spectroscopic members across all five dSphs. We confirm previous measurements of the velocity dispersions and dynamical masses, and we provide upper limits on bulk rotation. Our measurements confirm that M31 satellites obey the same relation between stellar mass and stellar metallicity as Milky Way (MW) satellites and other dwarf galaxies in the Local Group. The metallicity distributions show trends with stellar mass that are similar to those of MW satellites, including evidence in massive satellites for external influence, like pre-enrichment or gas accretion. We present the first measurements of individual element ratios, like [Si/Fe], in the M31 system, as well as measurements of the average [{alpha}/Fe] ratio. The trends of [{alpha}/Fe] with [Fe/H] also follow the same galaxy mass-dependent patterns as MW satellites. Less massive galaxies have more steeply declining slopes of [{alpha}/Fe] that begin at lower [Fe/H]. Finally, we compare the chemical evolution of M31 satellites to M31's Giant Stellar Stream and smooth halo. The properties of the M31 system support the theoretical prediction that the inner halo is composed primarily of massive galaxies that were accreted early. As a result, the inner halo exhibits higher [Fe/H] and [{alpha}/Fe] than surviving satellite galaxies.