It’s worth noting you do have to explicitly invoke your right to remain silent, because the legal system is horrible. If you don’t explicitly invoke your right to remain silent, your silence in response to questions can actually be cited in court of law as evidence of guilt.
You generally shouldn’t talk to cops at all, but you general script here is “Am I under arrest/being detained?”. If they answer yes, you have to say “I’m invoking my right to a publicly provided lawyer, and my right to remain silent.” (something similar to that, but try to keep it relatively formal, cops have argued before that incorrect phrasing means the right didn’t apply. See the “lawyer dog” case). And then you have to remain silent. If you talk at all, you’ve waived your right to remain silent, and you must reinvoke it when you’re done talking for it to apply. Cops are sneaky bastards and will try to get you to talk with friendly conversation or small things, don’t fall for it. If necessary, repeat “I have invoked my right to remain silent”. If you’ve invoked your right against self-incrimination, cops are not legally allowed to use your silence as evidence or suggestion of guilt in a court of law, and your publicly provided lawyer will know this. Also, no matter how under-funded and shit public lawyers can be, you do want yours.
It’s worth noting that the right to remain silent and the fifth are kind of distinct in practice. Your right to remain silent/non-incrimination applies in police custody. As a further note to that, cops will often ask questions to people not in custody specifically so they don’t have to deal with those rights- the correct answer to this is to not talk to cops. Never talk to a cop unless you’re detained, and then only to invoke your right to silence. The Fifth is invoked in court, and is the right to refuse to testify during your own trial. It’s invoked unconditionally- if you refuse to testify against yourself, you can’t testify for yourself. You can’t be a witness at all. If you testify for yourself, the prosecution can ask you whatever they want, and you do have to answer.
TLDR: America’s legal system is full of weird loopholes because cops are tricky bastards that can and will argue any absurd thing if it means they can put more people in prison. Don’t get tripped up by them.