Answer
Larger number is $9$.
Smaller number is $4$.
Work Step by Step
Let Larger number be $x$ and Smaller number be $y$.
Difference of two numbers is $5$
$x - y = 5$ Equation$(1)$
Twice the smaller number added to five times larger number is $53$.
$2y + 5x = 53$
$5x + 2y = 53$ Equation $(2)$
From Equation $(1)$ we get,
$x = y +5$
Substituting $x$ in Equation $(2)$
$5(y+5) + 2y = 53$
$5y+25 + 2y = 53$
$7y +25 = 53$
$7y = 53-25$
$7y = 28$
$y = 4$
Substituting $y$ value in Equation $(1)$,
$x - y = 5$
$x - 4 = 5$
$x = 5+4$
$x = 9$
Larger number is $9$.
Smaller number is $4$.