There are a number of situations that we can imagine in the present day where the 5th Amendment would be beneficial to citizens. Let us look at three of them.
First, we can imagine a situation in which the government wants to take someone’s property and give it to someone else. For example, imagine that you own a house in a bad area of town and some company wants to build a mall there to help redevelop the area. The government might try to force you to sell your home to the developer. (In fact, this was done in a case called Kelo v. City of New London.) You could hope to use the 5th Amendment to stop the government from doing this because the amendment says that the government can only force you to sell your land if it is for a public use.
Second, we can imagine a situation where you are caught up in an asset forfeiture situation. Let us say that you are married and the police believe that your spouse is selling drugs. The police can seize your house because it was being used in the commission of a crime. They do not even have to convict your spouse (let alone you) of a crime. You can try to fight this by claiming the protection of the 5th Amendment. The relevant part of this amendment says that you cannot have your property (or your life or liberty) taken without the due process of law. You can argue that this means that they have to at least have a trial where they prove a crime has been committed before they can seize your home.
Finally, we can imagine a situation in which you might be tried over and over for the same crime. Let us say that you are tried and acquitted of a crime. The government still thinks that you are guilty of the crime so they arrest you again and put you on trial again. You could fight this abuse by invoking the protection of the 5th Amendment, which says that you cannot be tried more than once for the same crime.
All of these are situations that could arise (or actually have arisen) today and for which you could try to use the 5th Amendment to protect you.