When adding and subtracting negative numbers, the sign of the second number needs to be taken into account.  

Turn the second number into a positive number. But if it was originally negative, then the sign of the operation also needs to be changed.

An easy way to remember what happens is to look at the sign of the operation and the sign of the second number. If they are both the same (plus-plus or minus-minus) then make the operation an addition. Otherwise it is a subtraction.

So 5 + -3 becomes 5 - 3 (signs are different). And 6 - -8 becomes 6 + 8 (signs are the same).