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The movie's musical score was composed by Brian Tyler (who composed Fast and Furious 3, 4, 5, and 7 lol). It is part of his original score made for the movie.
If you mean the soft, sad piece in the first few seconds, it is actually found on the Fast & Furious 4 soundtrack as the very last track (since the plot of Fast Five picks up immediately where Part 4 ended), called "Judgment":
Interestingly enough, that piece features a few seconds of what is called the "Brian and Mia" theme, written for Paul Walker and Jordana Brewster's characters in the series. It kind of ended up becoming the main theme of the movies since Part 4, which is fitting since --- if you think about it --- their romance in Part 1 formed the foundation for the entire franchise's story.