It should work as far as lining up the camera, volume buttons etc., but you may need to put a spacer of some sort if it is loose. There are several tutorials on you tube with suggestions. Good luck if you bid =)
Most notably, the camera and LED flash on the back of the iPhone 5s are different from the previous model. Depending on how the case fits around the camera, it could prevent the iPhone 5s camera from operating correctly.