Actually, THE STATE is not named in the 5th Amendment. That is the reason we have the 14th Amendment, to clear up the ambiguity.
But all along, by implication, all levels of government and individuals were always bound by the 5th Amendment's requirement to respect life.
The mention of life in 5th Amendment is a statement of principle, that the taking of innocent life is not to be found in the United States of America. Innocent blood is not to be shed by individuals, and not by the government.
Life must be respected, or society cannot function. States cannot make laws allowing the killing of innocents. The President cannot order the death of an innocent. Individuals cannot take life by their own hands.
Once we advocate blurring the lines, we're in trouble.
(Realizing that abortion blurred the lines, but only by unconstitutional judicial edict, and not by the will of the people.)
Read the amendment again. It has NOTHING to do with the conduct of individuals, only the government.