Given 5x – 1 < 24 and 5x + 1 > –24

Let us consider the first inequality.

5x – 1 < 24

⇒ 5x – 1 + 1 < 24 + 1

⇒ 5x < 25

⇒ x < 5

∴ x ∈ (–∞, 5) (1)

Now, let us consider the second inequality.

5x + 1 > –24

⇒ 5x + 1 – 1 > –24 – 1

⇒ 5x > –25

⇒ x > –5

∴ x ∈ (–5, ∞) (2)

From (1) and (2), we get

x ∈ (–∞, 5) ∩ (–5, ∞)

∴ x ∈ (–5, 5)

Thus, the solution of the given system of inequations is (–5, 5).