my answer also comes to be 2/35!!
I don't know how 1/35 is the answer

Here is an easy approach for these kinds of problems.
Instead of dealing with fractions, convert to whole numbers.
let the length of the stick be 7*5 = 35 units

Now the Fifths will be divided at the following marks.

5, 10, 15, 20, 25, 30, 35


The seventh's will be divided at the following marks

7, 14, 21, 28, 35

Now arrange these in ascending order.

5, 7, 10, 14, 15, 20, 21, 25,28, 35

The smallest difference between any two numbers is
1. ie. (15-14, 21-20)

When expressed as a fraction it is
1/35

Ht Helps

Thanks a lot vittal!!