1. **State the problem:** We need to solve the expression $\frac{1}{5} + \left(-\frac{4}{5}\right)$. 2. **Recall the rule for adding fractions with the same denominator:** When adding fractions with the same denominator, add the numerators and keep the denominator the same. 3. **Apply the rule:** $$\frac{1}{5} + \left(-\frac{4}{5}\right) = \frac{1 + (-4)}{5}$$ 4. **Simplify the numerator:** $$\frac{1 - 4}{5} = \frac{-3}{5}$$ 5. **Interpret the result:** The sum is $-\frac{3}{5}$, which lies between $-1$ and $0$ on the number line, closer to zero. **Final answer:** $$\boxed{-\frac{3}{5}}$$