Suppose we have the following two dice:

- a fair, five-sided die with numbers \(D_5 = [1,2,3, 4, 5]\)
- a fair, six-sided die with numbers \(D_6 = [1,2, 3, 4, 5, 6]\).

Does there exist a **different** pair of dice with 5 and 6 sides, such that the probability distribution of their sum is the same as rolling \( D_5 \) and \( D_6 \)?

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