Answer
$-\dfrac{15}{13} + \dfrac{10}{13}i$
Work Step by Step
Multiply both the numerator and the denominator by the conjugate of the denominator, which is $2+3i$, to obtain:
$=\dfrac{5i(2+3i)}{(2-3i)(2+3i)}
\\=\dfrac{10i+15i^2}{(2-3i)(2+3i)}$
Simplify using the rule $(a-b)(a+b)=a^2-b^2$ to obtain:
$=\dfrac{10i+15i^2}{2^2-(3i)^2}
\\=\dfrac{10i+15i^2}{4-9i^2}$
Use the fact that $i^2=-1$ to obtain:
$=\dfrac{10i+15(-1)}{4-9(-1)}
\\=\dfrac{10i-15}{4+9}
\\=\dfrac{-15+10i}{13}
\\=-\dfrac{15}{13} + \dfrac{10}{13}i$
