A temperature-dependent, single crystal x-ray diffraction study of the giant magnetocaloric material, ${\mathrm{Gd}}_5\left({\mathrm{Si}}_2{\mathrm{Ge}}_2\right)$, across its Curie temperature (276 K) reveals that the simultaneous orthorhombic to monoclinic transition occurs by a shear mechanism in which the $(\mathrm{Si},\mathrm{Ge})-(\mathrm{Si},\mathrm{Ge})$ dimers that are richer in Ge increase their distances by 0.859(3) Å and lead to twinning. The structural transition changes the electronic structure, and provides an atomic-level model for the change in magnetic behavior with temperature in the ${\mathrm{Gd}}_5({\mathrm{Si}}_x{\mathrm{Ge}}_{1-x}{)}_4$.