My simple solution was:

- Use a normal d5 and d6.

- On a roll, if the sum on the dice face is >= 7, add 1 to the sum.

If I roll 2+3, the result is 5. If I roll 3+4, the sum is 7, so add 1 to get the result of 8.

The gives you this distribution, and is simple in practice.

      1  2  3  4  5
    1 2  3  4  5  6
    2 3  4  5  6  8
    3 4  5  6  8  9
    4 5  6  8  9  10
    5 6  8  9  10 11
    6 8  9  10 11 12