Answer
$-\dfrac{1}{4}+\dfrac{5}{4}i$
Work Step by Step
Multiply both the numerator and the denominator by the conjugate of the denominator, which is $4i$, to obtain:
$=\dfrac{(5+i)(4i)}{-4i(4i)}
\\=\dfrac{20i+4i^2}{-16i^2}$
Use the fact that $i^2=-1$ to obtain:
$=\dfrac{20i+4(-1)}{-16(-1)}
\\=\dfrac{20i-4}{16}
\\=\dfrac{-4+20i}{16}
\\=-\dfrac{4}{16} + \dfrac{20}{16}i
\\=-\dfrac{1}{4}+\dfrac{5}{4}i$
