Answer
$\dfrac{17}{13}+\dfrac{7i}{13}$
Work Step by Step
Multiplying by the conjugate of the denominator of $
\dfrac{5-i}{3-2i}
$ results to
\begin{array}{l}
\dfrac{5-i}{3-2i}
\cdot
\dfrac{3+2i}{3+2i}
\\\\=
\dfrac{5(3)+5(2i)+(-i)(3)+(-i)(2i)}{(3)^2-(2i)^2}
\\\\=
\dfrac{15+10i-3i-2i^2}{9-4i^2}
\\\\=
\dfrac{15+10i-3i-2(-1)}{9-4(-1)}
\\\\=
\dfrac{17+7i}{13}
\\\\=
\dfrac{17}{13}+\dfrac{7i}{13}
.\end{array}