1. **State the problem:** Rationalise the denominator of the expression $$\frac{7 - \sqrt{5}}{\sqrt{5} - 2}$$ and express the answer in the form $$a + b\sqrt{5}$$. 2. **Formula and rule:** To rationalise a denominator with a surd, multiply numerator and denominator by the conjugate of the denominator. The conjugate of $$\sqrt{5} - 2$$ is $$\sqrt{5} + 2$$. 3. **Multiply numerator and denominator by the conjugate:** $$\frac{7 - \sqrt{5}}{\sqrt{5} - 2} \times \frac{\sqrt{5} + 2}{\sqrt{5} + 2} = \frac{(7 - \sqrt{5})(\sqrt{5} + 2)}{(\sqrt{5} - 2)(\sqrt{5} + 2)}$$ 4. **Simplify the denominator using difference of squares:** $$ (\sqrt{5})^2 - (2)^2 = 5 - 4 = 1 $$ 5. **Expand the numerator:** $$ (7)(\sqrt{5}) + 7 \times 2 - \sqrt{5} \times \sqrt{5} - \sqrt{5} \times 2 = 7\sqrt{5} + 14 - 5 - 2\sqrt{5} $$ 6. **Combine like terms in numerator:** $$ (7\sqrt{5} - 2\sqrt{5}) + (14 - 5) = 5\sqrt{5} + 9 $$ 7. **Write the final expression:** $$ \frac{5\sqrt{5} + 9}{1} = 9 + 5\sqrt{5} $$ **Final answer:** $$9 + 5\sqrt{5}$$