Imagine the die are coloured red and blue.

That the total is divisible by 5 means it is 5 or 10.

5 can be made by (r1,b4), (r2,b3), (r1,b4)

10 can be made (r4,b6), (r5,b5), (r6,b4)

These are all equally likely cases, so 1 in 6 cases where the total is divisible by 5 have both die showing 5, that is 1/6.

RonL