One number is three more than a second number. Three times the first is 13 less than 5 times the second.

14 and 11

let x be the second number then the first number = x + 3 (3 more than second)

Also 3 (x + 3) = 5x - 13

3x + 9 = 5x - 13

subtract 3x from both sides

9 = 5x - 3x - 13

9 = 2x - 13

add 13 to both sides

22 = 2x

divide both sides by 2

11 = x → second number

first number = x + 3 = 11 + 3 = 14