1. **State the problem:** Simplify and understand the expression $$\frac{2x^2}{\sqrt{x^3 + 5}}$$. 2. **Recall the rules:** The square root of a sum cannot be separated into the sum of square roots. We can rewrite the denominator as a power: $$\sqrt{x^3 + 5} = (x^3 + 5)^{\frac{1}{2}}$$. 3. **Rewrite the expression:** $$\frac{2x^2}{(x^3 + 5)^{\frac{1}{2}}}$$ 4. **Interpretation:** This is a rational expression with a polynomial numerator and a radical denominator. It cannot be simplified further without specific values for $x$. 5. **Domain considerations:** The expression is defined where the denominator is not zero and the radicand is non-negative: $$x^3 + 5 \geq 0 \implies x^3 \geq -5$$ 6. **Summary:** The expression is $$\frac{2x^2}{\sqrt{x^3 + 5}}$$ with domain $$x \geq -\sqrt[3]{5}$$. Final answer: $$\frac{2x^2}{\sqrt{x^3 + 5}}$$