Explanation

7¹⁰−5¹⁰ = 49⁵−25⁵. Modulo 11, 49 ≡ 5 and 25 ≡ 3, so this is 5⁵−3⁵ = 3125−243 = 2882 = 11·262, hence divisible by 11, option D. It is not divisible by 5 or 7 (check residues), and it ends in 4, so 10 is impossible.