Answer
$\left( -\infty,-\dfrac{15}{2} \right)$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To solve the given inequality, $
\dfrac{2x-5}{-4}\gt5
,$ use the properties of inequality.
For the interval notation, use a parenthesis for the symbols $\lt$ or $\gt.$ Use a bracket for the symbols $\le$ or $\ge.$
For graphing inequalities, use a hollowed dot for the symbols $\lt$ or $\gt.$ Use a solid dot for the symbols $\le$ or $\ge.$
$\bf{\text{Solution Details:}}$
Multiplying both sides by a negative number (and consequently reversing the sign), the inequality above is equivalent to
\begin{array}{l}\require{cancel}
-4\cdot\left( \dfrac{2x-5}{-4} \right)\lt-4\cdot5
\\\\
2x-5\lt-20
.\end{array}
Using the properties of inequality, the inequality above is equivalent to
\begin{array}{l}\require{cancel}
2x\lt-20+5
\\\\
2x\lt-15
\\\\
x\lt-\dfrac{15}{2}
.\end{array}
The red graph is the graph of the solution set.
In interval notation, the solution set is $
\left( -\infty,-\dfrac{15}{2} \right)
.$