1. **State the problem:** Simplify the radical expression $$5\sqrt{x^5 y^5}$$. 2. **Recall the rule for nth roots:** $$\sqrt[n]{a^n} = |a|$$ if $n$ is even, and $a$ if $n$ is odd. Since 5 is odd, $$\sqrt[5]{x^5} = x$$ and $$\sqrt[5]{y^5} = y$$. 3. **Apply the rule to the expression:** $$5\sqrt{x^5 y^5} = 5\sqrt{(xy)^5}$$ 4. **Simplify the fifth root:** $$5\sqrt{(xy)^5} = 5\sqrt[5]{(xy)^5} = 5xy$$ 5. **Final answer:** $$5xy$$ This is already in the form $A$, where $A = 5xy$ and no radical remains.