`5) 4/[\sqrt{5}-3]-1/[\sqrt{5}+2]`
`=[4(\sqrt{5}+3)]/[5-9]-[\sqrt{5}-2]/[5-4]`
`=-\sqrt{5}-3-\sqrt{5}+2`
`=-2\sqrt{5}-1`
`6)1/[3-2\sqrt{2}]+[2\sqrt{3}]/[2+\sqrt{5}]`
`=[3+2\sqrt{2}]/[9-8]+[2\sqrt{3}(2-\sqrt{5})]/[4-5]`
`=3+2\sqrt{2}-4\sqrt{3}+2\sqrt{15}`
5)
\(\dfrac{4}{\sqrt{5}-3}-\dfrac{1}{\sqrt{5}+2}\\ =\dfrac{4\left(\sqrt{5}+3\right)}{\left(\sqrt{5}+3\right)\left(\sqrt{5}-3\right)}-\dfrac{\sqrt{5}-2}{\left(\sqrt{5}-2\right)\left(\sqrt{5}+2\right)}\)
\(=\dfrac{4\sqrt{5}+12}{5-9}-\dfrac{\sqrt{5}-2}{5-4}\\ =\dfrac{4\sqrt{5}+12}{-4}-\left(\sqrt{5}-2\right)\\ =\dfrac{4\left(\sqrt{5}+3\right)}{-4}-\sqrt{5}+2\\ =-\left(\sqrt{5}+3\right)-\sqrt{5}+2\\ =-\sqrt{5}-3-\sqrt{5}+2\\ =-2\sqrt{5}-1\)
6)
\(\dfrac{1}{3-2\sqrt{2}}+\dfrac{2\sqrt{3}}{2+\sqrt{5}}\\ =\dfrac{3+2\sqrt{2}}{\left(3-2\sqrt{2}\right)\left(3+2\sqrt{2}\right)}+\dfrac{2\sqrt{3}\left(2-\sqrt{5}\right)}{\left(2+\sqrt{5}\right)\left(2-\sqrt{5}\right)}\)
\(=\dfrac{3+2\sqrt{2}}{9-8}+\dfrac{4\sqrt{3}-2\sqrt{15}}{4-5}\\ =3+2\sqrt{2}-\dfrac{4\sqrt{3}-2\sqrt{15}}{5-4}\\ =3+2\sqrt{2}-\left(4\sqrt{3}-2\sqrt{15}\right)\\ =3+2\sqrt{2}-4\sqrt{3}+2\sqrt{15}\)
