#### Answer

$\color{blue}{-\dfrac{11}{10}}$.

#### Work Step by Step

Multiply $2w+3$ to both sides of the equation to obtain:
$5(2w+3) = \dfrac{4}{2w+3} \cdot (2w+3)
\\5(2w)+5(3)=4
\\10w+15=4$
Subtract $15$ to both sides of the equation to obtain:
$10w=4-15
\\10w=-11$
Divide $10$ to both sides to obtain:
$w = -\frac{11}{10}$
Cheking:
$5=\dfrac{4}{2w+3}?
\\5 = \dfrac{4}{2\cdot(-\frac{11}{10})+3}?
\\5=\dfrac{4}{-\frac{11}{5}+3}?
\\5=\dfrac{4}{-\frac{11}{5} + \frac{15}{5}}?
\\5=\dfrac{4}{\frac{4}{5}}?
\\5=4 \cdot \frac{5}{4}?
\\5=5$
Thus, the solution to the given equation is: $\color{blue}{-\dfrac{11}{10}}$.