If the difference between two numbers is $\text{'}5\text{'}$  and difference between their squares is $\text{'}65\text{'}$ then the numbers are

Let $x$ ,$y$   be two numbers

Given $\left(x-y\right)=5\cdots \cdots \left(1\right)$

$x^2-y^2=65$

$\left(x-y\right)\left(x+y\right)=65\left(\because a^2-b^2=\left(a+b\right)\left(a-b\right)\right)$

$5\left(x+y\right)=65$

$x+y=\frac{65}{5}$

$x+y=13\cdots \cdots \left(2\right)$

$\left(1\right)+\left(2\right)$

$x=\frac{18}{2}$

$x=9$

$y=\frac{8}{2}$

$y=4$

$\therefore \left(x,y\right)=\left(9,4\right)$