1. **State the problem:** Simplify the expression $$2\sqrt{3} - 5 - \frac{11}{\sqrt{12} - 1}$$. 2. **Recall the formula and rule:** To simplify expressions with radicals in the denominator, multiply numerator and denominator by the conjugate of the denominator to rationalize it. 3. **Simplify the denominator's radical:** $$\sqrt{12} = \sqrt{4 \times 3} = 2\sqrt{3}$$. 4. **Rewrite the expression:** $$2\sqrt{3} - 5 - \frac{11}{2\sqrt{3} - 1}$$. 5. **Rationalize the denominator:** Multiply numerator and denominator by the conjugate $$2\sqrt{3} + 1$$: $$\frac{11}{2\sqrt{3} - 1} \times \frac{2\sqrt{3} + 1}{2\sqrt{3} + 1} = \frac{11(2\sqrt{3} + 1)}{(2\sqrt{3} - 1)(2\sqrt{3} + 1)}$$. 6. **Calculate the denominator using difference of squares:** $$(2\sqrt{3})^2 - 1^2 = 4 \times 3 - 1 = 12 - 1 = 11$$. 7. **Substitute back:** $$\frac{11(2\sqrt{3} + 1)}{11}$$. 8. **Cancel common factor 11:** $$\frac{\cancel{11}(2\sqrt{3} + 1)}{\cancel{11}} = 2\sqrt{3} + 1$$. 9. **Rewrite the original expression:** $$2\sqrt{3} - 5 - (2\sqrt{3} + 1)$$. 10. **Simplify by combining like terms:** $$2\sqrt{3} - 5 - 2\sqrt{3} - 1 = (2\sqrt{3} - 2\sqrt{3}) + (-5 - 1) = 0 - 6 = -6$$. **Final answer:** $$-6$$.