5. $f(x)=\frac{a x}{1+b x}, a \neq 1$. Then $f^{(n)}(x)=$ $\qquad$

Translate the above text into English, please retain the original text's line breaks and format, and output the translation result directly. 

5. $f(x)=\frac{a x}{1+b x}, a \neq 1$. Then $f^{(n)}(x)=$ $\qquad$
5. $f^{(n)}(x)=\frac{a^{n} x}{1+\frac{a^{n}-1}{a-1} b x}$ Hint: You can use the method of guess and prove.

将上面的文本翻译成英文，请保留源文本的换行和格式，直接输出翻译结果。

5. $f^{(n)}(x)=\frac{a^{n} x}{1+\frac{a^{n}-1}{a-1} b x}$ Hint: You can use the method of guess and prove.