4) $\dfrac{\sqrt{25.3} - 5 \sqrt{2}}{\sqrt{3}-\sqrt{2}} -\dfrac{2}{\sqrt{3}-1} + \dfrac{3}{\sqrt{3}}$

$= \dfrac{5\sqrt{3} - 5 \sqrt{2}}{\sqrt{3}-\sqrt{2}} -\dfrac{2}{\sqrt{3}-1} + \sqrt{3}$

$= \dfrac{5(\sqrt{3} - \sqrt{2})}{\sqrt{3}-\sqrt{2}} - \dfrac{2(\sqrt{3}+1)}{(\sqrt{3}-1)(\sqrt{3}+1)} + \sqrt{3}$

$= 5 + \dfrac{2\sqrt{3}+2}{2} + \sqrt{3}$

$=5+\sqrt{3}+1+\sqrt{3} = 6 + 2 \sqrt{3}$.

5) $(\dfrac{5-2\sqrt{5}}{2-\sqrt{5}} - 2)(\dfrac{5 + 3\sqrt{5}}{3 + \sqrt{5}}-2)$

$= (\dfrac{\sqrt{5}(\sqrt{5}-2)}{2-\sqrt{5}} - 2)(\dfrac{\sqrt{5}(\sqrt{5} + 3)}{3 + \sqrt{5}}-2)$

$=(-\sqrt{5}-2)(\sqrt{5}-2)$

$=-(\sqrt{5}+2)(\sqrt{5}-2) = -(5-4) = -1$.

6) $\dfrac{5 \sqrt{3} - 3 \sqrt{5}}{\sqrt{3}-\sqrt{5}}-\dfrac{1}{4 + \sqrt{15}} + 3 \dfrac{\sqrt{5}}{\sqrt{3}}$

$= \dfrac{ \sqrt{3} \sqrt{5} (\sqrt{5} - \sqrt{3})}{\sqrt{3}-\sqrt{5}}-\dfrac{4-\sqrt{15}}{(4+ \sqrt{15})(4-\sqrt{15})} + 3 \dfrac{\sqrt{5}}{\sqrt{3}}$

$= -\sqrt{15} - \dfrac{4-\sqrt{15}}{16-15} + 3 \dfrac{\sqrt{15}}{3}$

$=-\sqrt{15} -4 + \sqrt{15} + \sqrt{15}$

$= \sqrt{15}-4$.