It appears to be the brass buttplate of an Enfield Model-1853 Rifle, used by both sides in the American civil war. That ID is based on your brass buttplate's top-end and lower-end both being a "rounded" shape, and the location of the screw-holes, and the measurements of 5"-by-2" you reported (which seem to be rough estimates). On the ones I've dug, the width measured at the lower screw-hole is 1.77-inches.