ELI5: During a police interrogation, can you actually get away with not saying anything until you're provided with a lawyer?

Depends on where you live, but I assume you are talking about the United States.

In the US, the sixth amendment to the constitution says the following:

In all criminal prosecutions, the accused shall enjoy the right to a speedy and public trial, by an impartial jury of the State and district wherein the crime shall have been committed, which district shall have been previously ascertained by law, and to be informed of the nature and cause of the accusation; to be confronted with the witnesses against him; to have compulsory process for obtaining witnesses in his favor, and to have the Assistance of Counsel for his defence.

Brewer v. Williams (1979) held that once adversarial proceedings have begun against a defendant, he has a right to legal representation when the government interrogates him.

So basically, yes, it works like it does on TV. At least, it does in the States.

Now, in practical matters, the police are allowed to lie to you. There’s nothing stopping them from trying to convince you that you don’t need a lawyer. You could say to them something like “I think I need a lawyer,” and they could say something like “Why do you need a lawyer? Lawyers are for bad guys. You aren’t a bad guy, are you? We just want to get a bit of information”

Explain Like I`m Five: good questions, best answers.