The numbers are 1 and 18
Solution:
Let the smaller number be "x"
Let the larger number be "y"
Given that smaller of two numbers is five less than
the larger number
smaller number = one - third of larger number - 5

3x = y - 15
y = 3x + 15 ------- eqn 1
Half the larger added to the smaller is 10

y + 2x = 20 ------- eqn 2
Let us solve eqn 1 and eqn 2
Substitute eqn 1 in eqn 2
3x + 15 + 2x = 20
5x = 20 - 15
5x = 5
x = 1
From eqn 1,
y = 3(1) + 15 = 18
y = 18
Thus the numbers are 1 and 18