Inspired by Arjen Vreugdenhil

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 $D_6$ ?

Inspiration .