How to solve without a graphing calculator (if it's not allowed):
1) convert x+y= 5 to slope-intercept form. (right now it's in standard form.) We can do this by solving for y.
x+y=5 (subtract x from each side), y= -x +5
2) graph by hand using y=mx+b. From our equation, we can see that m= -1 and b=5. So, graph starting at 5, and go down one, over one, as far as you need to be able to draw the line through your points. Now, you can see that the y-intercept is 5 and the x-intercept is 5.