#### Answer

$a=12 \text{ } cm$

#### Work Step by Step

Using $a^2+b^2=c^2$ or the Pythagorean Theorem, then,
\begin{array}{l}\require{cancel}
a^2+5^2=13^2
\\\\
a^2+25=169
\\\\
a^2=169-25
\\\\
a^2=144
\\\\
a=\pm\sqrt{144}
\\\\
a=\pm\sqrt{(12)^2}
\\\\
a=\pm12
.\end{array}
Since there are no negative measurements, then $
a=12 \text{ } cm
.$