One important Supreme Court case that affected the due process clauses of the Fifth or Fourteenth Amendments is Miranda v. Arizona, as it established the requirement for law enforcement to inform suspects of their rights during custodial interrogations.

Miranda v. Arizona, a landmark case decided by the Supreme Court in 1966, had a significant impact on the due process clauses of the Fifth and Fourteenth Amendments. The court's decision in this case established the requirement for law enforcement officers to inform suspects of their rights during custodial interrogations, which became known as the "Miranda rights" or "Miranda warnings."

In the Miranda case, Ernesto Miranda was arrested and interrogated by the police regarding a kidnapping and . Miranda was not initially informed of his right to remain silent or his right to have an attorney present during questioning. During the interrogation, he confessed to the crimes and his confession was used as evidence against him during the trial.

The Supreme Court, in a 5-4 decision, ruled that Miranda's confession was obtained in violation of his Fifth Amendment right against self-incrimination. The Court held that the Fifth Amendment's protection against compelled self-incrimination requires law enforcement officers to inform suspects of their rights, known as the Miranda rights, before custodial interrogations. These rights include the right to remain silent, the right to an attorney, and the warning that anything the suspect says can be used against them in court.

The Miranda decision established the now-famous Miranda warnings, which must be given to suspects before any custodial interrogation takes place. Failure to provide these warnings can result in the exclusion of any resulting confessions or statements during trial. This case has had a lasting impact on the criminal justice system, protecting suspects' rights and ensuring that their coerced confessions are not used against them in court.