#### Answer

The solution is $(-3,0]$

#### Work Step by Step

$5x\le0$ and $-x+5\lt8$
Solve the first inequality:
$5x\le0$
Take $5$ to divide the right side:
$x\le\dfrac{0}{5}$
$x\le0$
Expressing in interval notation:
$(-\infty,0]$
Solve the second inequality:
$-x+5\lt8$
Take $5$ to the right side:
$-x\lt8-5$
$-x\lt3$
Change the sign on both sides and reverse the direction of the inequality sign:
$x\gt-3$
Expressing in interval notation:
$(-3,\infty)$
Since the compound inequality is formed by the word "and", the solution is composed by the numbers that satisfy both inequalities at the same time:
The solution is $(-\infty,0]\cap(-3,\infty)$
or
$(-3,0]$