Let $x$ and $y$ be positive real numbers such that $x + \frac{1}{y} = 5.$  Find the minimum value of $\frac{1}{x} + y.$
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Let $x$ and $y$ be positive real numbers such that $x + \frac{1}{y} = 5.$  Find the minimum value of $\frac{1}{x} + y.$
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
\frac{4}{5}
Let $x$ and $y$ be positive real numbers such that $x + \frac{1}{y} = 5.$  Find the minimum value of $\frac{1}{x} + y.$
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