In Leviticus 5, what was the only way to be cleansed after touching something unclean?

Les explains from Leviticus 5 that if a soul touched any unclean thing—whether the carcass of an unclean beast, unclean cattle, or unclean creeping things—and it was hidden from him, he was still unclean and guilty. Even something like picking up a dead bird while mowing the lawn made a person unclean. Les then points down to verse 6, where the only way he could overcome that situation was to bring his trespass offering unto the Lord for his sin which he had sinned. Les notes that nobody with a brain would do that, because this was not for us today; it was Israel under the Law. If someone had to go back to the Temple in Jerusalem every time he touched a dead animal, he would spend most of his time on overseas flights. But we do not, because we are not under that kind of Law. Les says this is just one example: over and over the Old Testament gives instructions that do not apply to us, and it would be ridiculous to try to keep all this. The Bible said it to Israel under the Law. Therefore it is appropriate to recognize that the Apostle Paul is the Gentile Apostle.