1. **State the problem:** Calculate the fifth root of the product of -32 and -243, i.e., find $$\sqrt[5]{(-32) \times (-243)}$$. 2. **Recall the formula:** The nth root of a product is the product of the nth roots: $$\sqrt[n]{a \times b} = \sqrt[n]{a} \times \sqrt[n]{b}$$. 3. **Calculate the product:** $$(-32) \times (-243) = 7776$$ because the product of two negative numbers is positive. 4. **Rewrite the problem:** Find $$\sqrt[5]{7776}$$. 5. **Prime factorize 7776:** $$7776 = 2^5 \times 3^5$$ 6. **Apply the fifth root:** $$\sqrt[5]{2^5 \times 3^5} = \sqrt[5]{2^5} \times \sqrt[5]{3^5} = 2 \times 3 = 6$$ 7. **Final answer:** $$\boxed{6}$$