Let the larger number be x and smaller number y.

given, sum of number is 35

⇒ x + y = 35 …[1]

Also, Four times the larger number is 5 more than 5 times the smaller number.

4x = 5y + 5 …[2]

Multiplying eq[1] by 5 and adding eq[2] to result, we get

5(x + y) + 4x = 175 + 5y + 5

⇒ 9x = 180

⇒ x = 20

From eq[1]

⇒ y = 15

∴ The larger number is 20 and the smaller number is 15.