1. The problem is to simplify the expression $\frac{5}{-3-\sqrt{3}}$. 2. To simplify expressions with radicals in the denominator, we multiply numerator and denominator by the conjugate of the denominator to rationalize it. 3. The conjugate of $-3-\sqrt{3}$ is $-3+\sqrt{3}$. 4. Multiply numerator and denominator by $-3+\sqrt{3}$: $$\frac{5}{-3-\sqrt{3}} \times \frac{-3+\sqrt{3}}{-3+\sqrt{3}} = \frac{5(-3+\sqrt{3})}{(-3)^2 - (\sqrt{3})^2}$$ 5. Calculate the denominator using difference of squares: $$9 - 3 = 6$$ 6. Expand the numerator: $$5(-3+\sqrt{3}) = -15 + 5\sqrt{3}$$ 7. So the expression becomes: $$\frac{-15 + 5\sqrt{3}}{6} = \frac{-15}{6} + \frac{5\sqrt{3}}{6} = -\frac{5}{2} + \frac{5\sqrt{3}}{6}$$ 8. This is the simplified form of the original expression. Final answer: $$-\frac{5}{2} + \frac{5\sqrt{3}}{6}$$