Answer
$x+5-\displaystyle \frac{10}{2x+3}$
Work Step by Step
$\begin{array}{ccccccccccc}
& &x & +5 & & \\
& &--&--&--& \\
2x+3&) & 2x^{2} & +13x& +5 & \\
& & 2x^{2} & +3x& & \color{red}{\leftarrow \small{x(2x+3) } } \\
& &--&-- & & \color{red}{ \small{subtract}} \\
& & & 10x& +5 & \\
& & & 10x & +15& \color{red}{\leftarrow \small{5(2x+3) } }\\
& & &--&-- & \color{red}{ \small{subtract}} \\
& & & & -10 &\\
\end{array}$
Quotient = $x+5$
Remainder = $-10$.
$\displaystyle \frac{dividend}{divisor}=quotient+\frac{remainder}{divisor}$
$\displaystyle \frac{ 2x^{2} +13x +5}{2x+3}$ = $x+5-\displaystyle \frac{10}{2x+3}$
