"No person shall be held to answer for a capital, or otherwise infamous crime, unless on a presentment or indictment of a Grand Jury, except in cases arising in the land or naval forces, or in the Militia, when in actual service in time of War or public danger; nor shall any person be subject for the same offense to be twice put in jeopardy of life or limb; nor shall be compelled in any criminal case to be a witness against himself, nor be deprived of life, liberty, or property, without due process of law; nor shall private property be taken for public use, without just compensation."
The relevant bit here is the part about being a witness against yourself. You can't remain silent when asked for identification, but you don't have to answer the cop when he asks you if you know how fast you were going. In that situation, you're pleading your 5th amendment right.
"No person shall be held to answer for a capital, or otherwise infamous crime, unless on a presentment or indictment of a Grand Jury, except in cases arising in the land or naval forces, or in the Militia, when in actual service in time of War or public danger; nor shall any person be subject for the same offense to be twice put in jeopardy of life or limb; nor shall be compelled in any criminal case to be a witness against himself, nor be deprived of life, liberty, or property, without due process of law; nor shall private property be taken for public use, without just compensation."
The relevant bit here is the part about being a witness against yourself. You can't remain silent when asked for identification, but you don't have to answer the cop when he asks you if you know how fast you were going. In that situation, you're pleading your 5th amendment right.