Final answer:
The United States Supreme Court case that held that a person accused of crimes must be advised of their Fifth and Sixth Amendment rights upon their arrest is Miranda v. Arizona (1966).
Step-by-step explanation:
The United States Supreme Court case that held that a person accused of crimes must be advised of their Fifth and Sixth Amendment rights upon their arrest is Miranda v. Arizona (1966). In this case, Ernesto Miranda was arrested and confessed to kidnapping without being informed of his right to remain silent and his right to an attorney. The Supreme Court ruled that suspects must be informed of these rights in order to ensure their statements are given voluntarily.