Answer
$5i-1$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To divide the given expression, $
\dfrac{5+i}{-i}
,$ multiply both the numerator and the denominator by $i$. Use $i^2=-1.$
$\bf{\text{Solution Details:}}$
Multiplying both the numerator and the denominator by $i,$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
\dfrac{5+i}{-i}\cdot\dfrac{i}{i}
\\\\=
\dfrac{(5+i)i}{-i^2}
.\end{array}
Using the Distributive Property which is given by $a(b+c)=ab+ac,$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
\dfrac{(5)i+(i)i}{-i^2}
\\\\=
\dfrac{5i+i^2}{-i^2}
.\end{array}
Since $i^2=-1,$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
\dfrac{5i+(-1)}{-(-1)}
\\\\=
\dfrac{5i-1}{1}
\\\\=
5i-1
.\end{array}
