Multiply the top and bottom by \sqrt{6}-\sqrt{5} to get 5/(\sqrt{6}+\sqrt{5})=\frac{5(\sqrt{6}-\sqrt{5})}{6-5}=5\sqrt{6}-5\sqrt{5}.
In general, \frac{a}{\sqrt{b}+\sqrt{c}}=\frac{a(\sqrt{b}-\sqrt{c})}{b-c} when b is not equal to c. In the case where b=c>0, then \frac{a}{\sqrt{b}+\sqrt{c}}=\frac{a}{2\sqrt{b}}=\frac{a\sqrt{b}}{2b}.