let x and y be the two consecutive numbers and y>x

since the numbers are consecutive we can write

y = x + 1

One third of the sum of two concecutive integers is 5 less than the smaller integer

(1/3)(x + y) = x - 5

plug y = x + 1 into the previous equation

(1/3)(x + x + 1) = x - 5

by solving the equation we find

x = 16

click here to see the step by step solution of the equation

y = x + 1 = 16 + 1 = 17

the numbers are 16 and 17.