Answer
$x+3$
Work Step by Step
$\begin{array}{ccccccccccc}
& &x & +3 & & \\
& &--& -- & -- & -- \\
x+5&) &x^{2} &+8x& +15 & \\
& &x^{2} & +5x& & \color{red}{\leftarrow \small{x(x+5) } } \\ \
& &--& -- & & \color{red}{ \small{subtract}} \\
& & & 3x & +15 & \\
& & & 3x & +15 & \color{red}{\leftarrow \small{3(x+5) } } \\ \
& & &--& -- & \color{red}{ \small{subtract}} \\
& & & & 0 &
\end{array}$
Quotient is $x+3$,
Remainder is $0$.
$\displaystyle \frac{dividend}{divisor}=quotient+\frac{remainder}{divisor}$
$\displaystyle \frac{x^{2} +8x +15}{x+5}$ = $x+3$
