The basis for the decision in Miranda v. Arizona, 384 US 436 (1966) was protection of Fifth and Sixth Amendment rights.
Explanation
The Miranda rights actually are not a Constitutional Amendment. They are based on a Supreme Court case, Miranda v. Arizona(1966).
In this case, Ernest Miranda had confessed to robbery and attempted rape, and this confession was offered as evidence in court to convict him. However, the Fifth Amendment guarantees that an accused person must not be compelled to testify against himself, and the Sixth Amendment guarantees the right to a speedy trial by jury and to legal counsel. The Supreme Court overturned Miranda's conviction, stating:
"The person in custody must, prior to interrogation, be clearly informed that he has the right to remain silent, and that anything he says will be used against him in court; he must be clearly informed that he has the right to consult with a lawyer and to have the lawyer with him during interrogation, and that, if he is indigent, a lawyer will be appointed to represent him."
Essentially, those accused of a crime must be informed of their rights (to remain silent and to have a lawyer) when they are arrested, before being questioned by the police.
So, Miranda rights are not the direct result of a Constitutional Amendment, but they are based off of the Fifth and Sixth Amendments.
Update
The Miranda ruling has been revised somewhat by subsequent Supreme Court decisions. On June 1, 2010, the Roberts' Court released the opinion for Berghuis v. Thompkins,08-1470 (2010), which held a defendant must demonstrably invoke his right to remain silent (by actually stating he wants to remain silent), rather than simply waive it.
5th- self-incrimination
6th- right to a lawyer
The FIfth and Sixth Amendments were involved in both cases.
The Miranda rights themselves are a part of the amendments to the Constitution. They became "the Miranda rights" and it was required that they be read to suspects in 1966. This was decided in the supreme court case Miranda v. Arizona.
Miranda v. Arizona
1966
Miranda v. Arizona
It affirmed the right to an attorney and was a case that led to the Miranda Rights that came about in Miranda vs Arizona.
Miranda v. Arizona, 384 US 436 (1966)
Miranda v. Arizona
Miranda v. Arizona, 384 US 436 (1966)Miranda v. Arizona, (1966) was the landmark Supreme Court case in which the court declared that the Fifth Amendment to the Constitution of the United States of America, (which also applies to the states through application of the Fourteenth Amendment) required that before law enforcement officers attempt to interrogate the accused, they inform the accused of their rights. These rights are now referred to as Miranda rights.
Miranda v. Arizona, 384 US 436 (1966)Ernesto Miranda was the plaintiff; the state of Arizona was the defendant. In a court case, the plaintiff/petitioner's name is always listed first, and the defendant/respondent's name is listed last.
The amendments to the Constitution contain the Miranda rights. The 5th amendment protects from self-incrimination, which is the right to remain silent. The 6th amendment asserts the right to an attorney, whether or not the suspect can afford one.
Miranda v. Arizona, 384 US 436 (1966)Miranda vs. Arizona
First amendment