One of the simplest ways is to draw the graph and manually the intercept.

Another way is to set in turn x = 0 and y = 0.

Using x = 0, we get 0 = -5. Since that is not true, there is no intercept.
Using y = 0, we get x = -5. That's your intercept and has coordinates (-5, 0)

x and y intercepts of the line y+3=16(x-2)

the answer in the back of books has the x is (35/16,0) y is (9,-35)

In your equation, put y = 0 and solve for x to find the x-intercept. (The y coordinates is 0)

Similarly, put x = 0 and solve for y to find the y-intercept. (The x-coordinates is 0)