#### Answer

$12$

#### Work Step by Step

According to the Pythagoras Theorem, if $a$ and $b$ are the lengths of the legs of a right triangle, and $c$ is the length of the
hypotenuse, then $a^{2}+b^{2}=c^{2}$.
Since $a=5$ and $c=13$, we substitute these values in the formula and solve:
$c^{2}=a^{2}+b^{2}$
$13^{2}=5^{2}+b^{2}$
$169=25+b^{2}$
$b^{2}=169-25=144$
Therefore, $b=\sqrt (144)=12$
Since $b$ represents a length, we assume that $b$ is positive and is equal to $12$.