1. **State the problem:** We have a map scale of 1:100,000, meaning 1 cm on the map represents 100,000 cm in reality. 2. **Formula and explanation:** The real distance $D$ is given by multiplying the map distance $d$ by the scale factor $S$: $$D = d \times S$$ where $d = 5$ cm and $S = 100,000$. 3. **Calculate the real distance in centimeters:** $$D = 5 \times 100,000 = 500,000 \text{ cm}$$ 4. **Convert centimeters to kilometers:** Recall that $100,000$ cm = 1 km, so: $$\frac{500,000 \text{ cm}}{100,000} = 5 \text{ km}$$ 5. **Final answer:** The distance represented by 5 cm on the map is **5 kilometers**.