Question

how do you graph f(x)=sin(x)-5

Answer 1

same way you'd graph any function: pick a few values for x, calculate y, and plot the point (x,y).

Of course, it helps to pick points which will show the shape of the graph with minimum effort. In this case, since you know something about the shape of sine waves, it will help to pick x at values like

0, pi/2, pi, 3pi/2, 2pi, etc.

Since the amplitude is 1, and the whole graph is shifted down by 5, the points to use will be

(0,-5)
(pi/2,-4)
(pi,-5)
(3pi/2,-6)
(2pi,-5)

Those will be the crests and troughs over a single period. Plot them and draw a wavy line through them. If still in doubt, review your graphs of sine waves.