1. **State the problem:** Simplify the expression $$\frac{1}{10x^3} + \frac{1}{5}$$ where the fractions are added. 2. **Formula and rules:** To add fractions, they must have a common denominator. The formula for adding fractions $$\frac{a}{b} + \frac{c}{d}$$ is $$\frac{ad + bc}{bd}$$. 3. **Find the common denominator:** The denominators are $$10x^3$$ and $$5$$. The least common denominator (LCD) is $$10x^3$$ because $$10x^3$$ is a multiple of $$5$$ (since $$10x^3 = 2 \times 5 \times x^3$$). 4. **Rewrite the second fraction with the LCD:** $$\frac{1}{5} = \frac{1 \times 2x^3}{5 \times 2x^3} = \frac{2x^3}{10x^3}$$ 5. **Add the fractions:** $$\frac{1}{10x^3} + \frac{2x^3}{10x^3} = \frac{1 + 2x^3}{10x^3}$$ 6. **Final answer:** $$\boxed{\frac{1 + 2x^3}{10x^3}}$$