Explanation

Factor out the smallest power: 5¹⁷ + 5¹⁸ + 5¹⁹ + 5²⁰ = 5¹⁷(1 + 5 + 5² + 5³). The bracket sums to 1 + 5 + 25 + 125 = 156. Since 156 = 12 × 13, the whole expression is a multiple of 13 regardless of the power of 5. Hence the number is divisible by 13, option (D).