#### Answer

The required function is
$$f(x)=-\frac{4}{5}x+5.$$

#### Work Step by Step

The equation of the linear function passing through points $P(x_1,y_1)$ and $Q(x_2,y_2)$ is given by
$$y=\frac{y_2-y_1}{x_2-x_1}(x-x_1)+y_1.$$
Using the data given in the problem:
$$x_1=0,\quad y_1=5,\quad x_2=5,\quad y_2=1$$
we have
$$y=\frac{1-5}{5-0}(x-0)+5$$
giving
$$y=-\frac{4}{5}x+5,$$
so our linear function is
$$f(x)=-\frac{4}{5}x+5.$$