1. **State the problem:** We know that five bottles have a total capacity of 1560 cm³. We need to find the total capacity of nine similar bottles. 2. **Identify the formula:** Since the bottles are similar, the capacity is proportional to the number of bottles. So, if 5 bottles have capacity 1560 cm³, then 1 bottle has capacity $ \frac{1560}{5} $ cm³. 3. **Calculate the capacity of one bottle:** $$ \text{Capacity of one bottle} = \frac{1560}{5} = 312 \text{ cm}^3 $$ 4. **Calculate the capacity of nine bottles:** $$ \text{Total capacity of 9 bottles} = 9 \times 312 = 2808 \text{ cm}^3 $$ 5. **Final answer:** The total capacity of nine similar bottles is $2808$ cm³.