Prove that the function `f(x) = 5x-3` is continuous at `x = 0`, at `x = -3` and at `x = 5`.

Explanation

To prove that the function \( f(x) = 5x - 3 \) is continuous at the points \( x = 0 \), \( x = -3 \), and \( x = 5 \), we need to show that the left-hand limit, right-hand limit, and the functional value at each of these points are equal.

### Step 1: Check continuity at \( x = 0 \)

1. **Left-hand limit**:
\[ \lim_{x \to 0^-} f(x) = \lim_{x \to 0^-} (5x - 3) = 5(0) - 3 = -3 \]
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