1. **State the problem:** We need to simplify the expression $$\frac{3 \sqrt{3}}{5 \sqrt{75}}$$. 2. **Recall the rules:** Simplify square roots and fractions by factoring and canceling common terms. 3. **Simplify the denominator:** $$\sqrt{75} = \sqrt{25 \times 3} = \sqrt{25} \times \sqrt{3} = 5 \sqrt{3}$$ 4. **Rewrite the expression:** $$\frac{3 \sqrt{3}}{5 \times 5 \sqrt{3}} = \frac{3 \sqrt{3}}{25 \sqrt{3}}$$ 5. **Cancel common factors:** $$\frac{3 \cancel{\sqrt{3}}}{25 \cancel{\sqrt{3}}} = \frac{3}{25}$$ 6. **Final answer:** $$\frac{3}{25}$$