1. **State the problem:** Simplify the expression $2x^2 \cdot 5x^3$. 2. **Recall the multiplication rules:** When multiplying terms with the same base, multiply the coefficients and add the exponents: $$a^m \cdot a^n = a^{m+n}$$ 3. **Multiply the coefficients:** $$2 \cdot 5 = 10$$ 4. **Add the exponents of $x$:** $$x^2 \cdot x^3 = x^{2+3} = x^5$$ 5. **Combine the results:** $$2x^2 \cdot 5x^3 = 10x^5$$ 6. **Final answer:** $10x^5$ is the simplified form.