$($a$)$ For $f(x)=\frac{5}{x},$ find the equation of the secant line through the points where $x=1$ and $x=5.$

$($b$)$ For $f(x)=\frac{5}{x},$ find the equation of the tangent line when $x=1.$

$($a$)$ Find the slope of the secant line of $f(x)=\frac{5}{x}$ by computing the average rate of change of $f(x)=\frac{5}{x}$ from $x=1$ to $x=5.$

The slope of the secant line is $$

$($Type an integer or a simplified fraction.$)$

The equation of the secant line is $y=$

$($b$)$ Find the slope of the tangent line of $f(x)=\frac{5}{x}$ by computing the instantaneous rate of change of $f(x)=\frac{5}{x}$ at $x=1.$

The slope of the tangent line is $$

$($Type an integer or a simplified fraction.$)$

The equation of the tangent line is $y=$