Legal Question in Constitutional Law in New Jersey

Except where it expressly limits what states can do, the Constitution applies only to the federal government. There is no such language in the Fifth Amendment, but there is in the Fourteenth.

Section one of the Fourteenth Amendment repeats some terms of the Fifth Amendment (including its Due Process clause) and says they apply to the states. It also forbids states to "make or enforce any law which shall abridge the privileges or immunities of citizens of the United States." That clause means the states must honor essentially all of the Bill of Rights. It also means states are bound by federal cases which interpret the Bill of Rights, including the Fifth Amendment's Due Process clause. So even if a particular case was only about the federal government and was based solely on the Fifth Amendment, states must follow it because the Fourteenth Amendment says they must.

You asked if "both amendments functionally apply to the states equally now." The language of the Fifth Amendment has not been changed, so it still doesn't apply to the states on its own. The Fourteenth Amendment could conceivably be altered or repealed some day; if that happens, and if the Fifth Amendment remains in place, it still would apply only to the federal government and not to the states.