Answer
$\dfrac{5}{13}+\dfrac{12}{13}i$
Work Step by Step
Multiply both the denominator and the numerator by $5+12i$, which is the conjugate of $5-12i$, to obtain:
\begin{align*}
\frac{13}{5-12i}\cdot \frac{5+12i}{5+12i}&=\frac{13(5+12i)}{(5-12i)(5+12i)}\\
\\&=\frac{13(5)+13(12i)}{5^2+12^2}&(\text{note that:}(a-bi)(a+bi)=a^2+b^2)\\
\\&=\frac{65+156i}{25+144}\\
\\&=\frac{65}{169}+\frac{156}{169}i \\
\\&=\frac{5}{13}+\frac{12}{13}i
\end{align*}
