1. **State the problem:** Racer jogged $5 \frac{3}{5}$ kilometers in 7 hours. We need to find his average speed in kilometers per hour. 2. **Convert mixed number to improper fraction:** $$5 \frac{3}{5} = \frac{5 \times 5 + 3}{5} = \frac{25 + 3}{5} = \frac{28}{5}$$ 3. **Use the formula for average speed:** $$\text{Average speed} = \frac{\text{Total distance}}{\text{Total time}}$$ 4. **Substitute values:** $$\text{Average speed} = \frac{\frac{28}{5}}{7}$$ 5. **Divide by 7:** $$\frac{\frac{28}{5}}{7} = \frac{28}{5} \times \frac{1}{7} = \frac{28 \times 1}{5 \times 7} = \frac{28}{35}$$ 6. **Simplify the fraction:** $$\frac{\cancel{28}^{4} \times 7}{\cancel{35}^{5} \times 7} = \frac{4}{5}$$ 7. **Convert to decimal or mixed number:** $$\frac{4}{5} = 0.8$$ **Final answer:** Racer's average speed is $0.8$ kilometers per hour.