What the Fifth Amendment says is that no person shall be deprived of life, liberty, or property without due process of law. Thats proper.
Concur, even more, the 5th Amendment states: "nor shall any person be subject for the same offense to be twice put in jeopardy of life or limb;"
This indicates that loss of life (as well as limbs) was considered neither cruel nor unusual.
So according to the Constitution it is unlawful to execute someone twice — at least for the same crime.