Answer
$$y'=5(x+\frac{1}{x})^4(1-\frac{1}{x^2})$$
Work Step by Step
$$y'=((x+\frac{1}{x})^5)'=5(x+\frac{1}{x})^{4}\cdot(x+\frac{1}{x})'=
5(x+\frac{1}{x})^4(1+(-\frac{1}{x^2})=5(x+\frac{1}{x})^4(1-\frac{1}{x^2})$$
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