ALGEBRA | Engineering Mathematics

Let $s$ be the side of the square and $d$ be the diagonal.

Thus;
$d=s+5$

$d^2=s^2+s^2$

$(s+5{)}^2=s^2+s^2$

$s^2+10s+25=2s^2$

$s^2-10s-25=0$

$d={\displaystyle \frac{10+\sqrt{100+100}}{2}}$

$d=5+5\sqrt{2}$ANSWER