Double Jeopardy Question?

One of my students asked a good question today about the 5th amendment's double jeopardy law, which states that a person can't be tried for the same crime twice using the same facts. If a person is put on a trial and found not guilty of a murder, but later on they find DNA evidence linking that person to the murder, does the double jeopardy rule still apply? Some websites say yes, that you can't be tried twice for the same crime, so that's why prosecutors want to get all the evidence they can the first time around. Yet other websites say no, the double jeopardy rule does NOT apply because even though you are putting the person on trial twice for the same crime, you are using DIFFERENT evidence, not the same set of facts you used in the first trial. Is anyone on here familiar with law (not speculating)? Thanks.