Sometimes it helps to think of subtraction in terms of "movement". Subtracting some positive amount is the same thing as moving left 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 then 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.