Solve the inequalities and represent the solution graphically on a number line:
$5x + 1 > -24, 5x - 1 < 24$

(N/A) $5x + 1 > -24 \Rightarrow 5x > -25$
$\Rightarrow x > -5$ ..... $(1)$
$5x - 1 < 24 \Rightarrow 5x < 25$
$\Rightarrow x < 5$ ..... $(2)$
From $(1)$ and $(2)$,it can be concluded that the solution set for the given system of inequalities is $(-5, 5)$. The solution of the given system of inequalities can be represented on a number line as shown below:
(The number line shows an open interval between $-5$ and $5$,with open circles at $-5$ and $5$ indicating that these points are not included in the solution set.)