1. **State the problem:** Simplify the expression $$\sqrt{25x^4}$$ assuming $$x > 0$$. 2. **Recall the formula:** The square root of a product is the product of the square roots: $$\sqrt{ab} = \sqrt{a} \times \sqrt{b}$$. 3. **Apply the formula:** $$\sqrt{25x^4} = \sqrt{25} \times \sqrt{x^4}$$ 4. **Simplify each square root:** $$\sqrt{25} = 5$$ because $$5^2 = 25$$. Since $$x > 0$$, $$\sqrt{x^4} = x^{\frac{4}{2}} = x^2$$. 5. **Combine the results:** $$5 \times x^2 = 5x^2$$ 6. **Final answer:** $$\boxed{5x^2}$$