The exact words in this amendment say, “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 offence 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.”
This amendment was made in the 18th century, some time in 1791, to protect the privileges of the citizens over the cruel government. It was important then and still is now because it gives people the right to be tried by a jury for committed crimes, the choice to be tried twice for doing the same felony, and the opportunity to gain something from their loss of their private property due to being used for public use. For example: if part of your yard was to be demolished in order to build a new road on your street, you would have the right to receive something/compensation in return from the government because they took your private property for public use.
There is a term called “pleading the fifth.” When you plead the fifth, you are using your Fifth Amendment right to not incriminate yourself with testimony. The Fifth Amendment says you have the right to not testify and incriminate yourself. It means you don't want to say anything that might make you look bad or sound guilty.