1. **State the problem:** Simplify the sum $$\frac{4}{m} + \frac{1}{m}$$. 2. **Formula and rules:** When adding fractions with the same denominator, add the numerators and keep the denominator the same: $$\frac{a}{c} + \frac{b}{c} = \frac{a+b}{c}$$ 3. **Apply the formula:** Here, both fractions have denominator $m$, so: $$\frac{4}{m} + \frac{1}{m} = \frac{4+1}{m} = \frac{5}{m}$$ 4. **Check for simplification:** The fraction $$\frac{5}{m}$$ cannot be simplified further since 5 and $m$ have no common factors. 5. **Final answer:** The simplified sum is $$\frac{5}{m}$$, which corresponds to option c.