5. Simplify $C_{n}^{0} C_{n}^{1}+C_{n}^{1} C_{n}^{2}+\cdots+C_{n}^{n-1} C_{n}^{n}=$
5. $C_{2 n}^{n-1}$ Consider the coefficient of $x^{n-1}$ in the expansion of $(1+x)^{2 n}$. On one hand, it equals $C_{2 n}^{n-1}$; on the other hand, $(1+x)^{2 n}=(1+x)^{n} \cdot(1+x)^{n}=\left(C_{n}^{0}+C_{n}^{1} x+C_{n}^{2} x^{2}+\cdots+C_{n}^{n-1} x^{n-1}+C_{n}^{n} x^{n}\right)\left(C_{n}^{0} x^{n}+C_{n}^{1} x^{n-1}+\cdots+C_{n}^{n-1} x+C_{n}^{n}\right)$, the coefficient of $x^{n-1}$ is $C_{n}^{0} C_{n}^{1}+C_{n}^{1} C_{n}^{2}+\cdots+C_{n}^{n-1} C_{n}^{n}$.