1. **State the problem:** Evaluate the limit $$\lim_{x \to 0} \frac{\sin x}{5x}$$. 2. **Recall the standard limit:** We know that $$\lim_{x \to 0} \frac{\sin x}{x} = 1$$. 3. **Rewrite the given limit to use this fact:** $$\lim_{x \to 0} \frac{\sin x}{5x} = \lim_{x \to 0} \frac{\sin x}{x} \cdot \frac{1}{5} = \left( \lim_{x \to 0} \frac{\sin x}{x} \right) \cdot \frac{1}{5}$$ 4. **Evaluate the limits:** $$= 1 \cdot \frac{1}{5} = \frac{1}{5}$$ 5. **Conclusion:** The value of the limit is $$\frac{1}{5}$$.