Now multiply x by (x+5) and place the product directly under x^2-2x-35
      _x___________
x+5 |x^2-2x-35
      -(x^2+5x)<---------remember the negative distributes

So subtract (x^2+5x) from x^2-2x-35 and you get 0x^2-7x
      _x___________
x+5 |x^2-2x-35
      -(x^2+5x)
      ----------
      0x^2-7x

Now the question is: how many times does x+5 go into -7x? The answer is -7 (x*(-7)=-7x)
      _x__-7________
x+5 |x^2-2x-35
      -(x^2+5x)
      ----------
      0x^2-7x-35<---------remember to pull down another part of the dividend

Multiply -7 by (x+5) to get -7x-35 and place it under -7x-35
      _x__-7________
x+5 |x^2-2x-35
      -(x^2+5x)
      ----------
      0x^2-7x-35
            -(7x-35)
            --------
                      0

So your answer is (x-7).
To verify you can multiply (x-7) by (x+5)

check: FOIL these factors

this verifies our answer

If you want to compute this answer quickly to check your work, check out http://www.calc101.com/webMathematica/long-divide.jsp. This page has a polynomial division calculator that allows you to do this quickly and shows its steps.