Sometimes it helps to think of subtraction in terms of "movement". Subtracting some positive amount is the same thing as moving <em>left </em>on the number line. If we start on the number 5 and move 7 to the left, you can see that we pass zero and end up 2 in the negative, so 5 - 7 = -2.
Another way to think about this is to look at subtracting 7 as subtracting 5 and <em>then </em>subtracting another two from 5 -- 5 - 5 - 2, in other words. 5 - 5 = 0, and 0 - 2 = -2, so we end up at the same place.