Which amendment guarantees that no one can be deprived of life or liberty without due process?

The correct choice highlights the essential principle of due process found within the 5th Amendment of the United States Constitution. This amendment asserts that no individual shall be "deprived of life, liberty, or property, without due process of law." This foundational clause ensures that legal processes are followed fairly before someone can be deprived of their basic rights. It serves as a protection against arbitrary or unjust government actions, emphasizing the need for legal procedures and safeguards.

The 5th Amendment is critical in the context of criminal justice and corrections, as it establishes the requirement that individuals are entitled to a fair trial and legal representation, ensuring that any deprivation of liberty is carried out lawfully. This is fundamental in the context of a jailer's responsibilities, as it pertains to the treatment of inmates and the legal standards that must be upheld during incarceration.

The other amendments mentioned focus on different rights—such as freedom of expression, cruel and unusual punishment, or state obligations concerning due process, but the specific wording regarding life, liberty, and the requirement of due process directly pertains to the 5th Amendment.