1. **State the problem:** Rationalise the denominator of the fraction $$\frac{1}{5 + \sqrt{3}}$$ and simplify the result. 2. **Formula and rule:** To rationalise a denominator with a surd (square root), multiply numerator and denominator by the conjugate of the denominator. The conjugate of $$5 + \sqrt{3}$$ is $$5 - \sqrt{3}$$. 3. **Multiply numerator and denominator by the conjugate:** $$\frac{1}{5 + \sqrt{3}} \times \frac{5 - \sqrt{3}}{5 - \sqrt{3}} = \frac{5 - \sqrt{3}}{(5 + \sqrt{3})(5 - \sqrt{3})}$$ 4. **Simplify the denominator using difference of squares:** $$(5 + \sqrt{3})(5 - \sqrt{3}) = 5^2 - (\sqrt{3})^2 = 25 - 3 = 22$$ 5. **Write the simplified expression:** $$\frac{5 - \sqrt{3}}{22}$$ 6. **Final answer:** The rationalised and simplified form of $$\frac{1}{5 + \sqrt{3}}$$ is $$\frac{5 - \sqrt{3}}{22}$$.