solution: $f^{-1}\left(\frac{1}{5}\right)$ is defined as the number $x$ such that $f(x)=\frac{1}{5}$. Thus, we solve the equation $$\frac{2}{x+1} = \frac{1}{5}.$$Multiplying both sides by $5(x+1)$, we have $$10 = x+1.$$Subtracting $1$ from both sides gives $x=\boxed{9}$.
prompt.content: <|im_start|>system
  You are a helpful assistant.<|im_end|>
  <|im_start|>user
  If $f(x)=\dfrac{2}{x+1}$, then what is the value of $f^{-1}\left(\frac{1}{5}\right)$?
  Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
  <|im_start|>assistant
  
prompt.role: user
extra_info.answer: 9
extra_info.question: If $f(x)=\dfrac{2}{x+1}$, then what is the value of $f^{-1}\left(\frac{1}{5}\right)$?
extra_info.split: test