I am having some trouble understanding how you determine which sign to use
why does the -5 in problem 2 become positive and the -6 in problem 3 stay negative they both have +-
You will need to provide more information. Perhaps write out the problems you are talking about. If a negative number becomes positive, it will be multiplied by a negative. And if a negative number stays negative, it is multiplied by a positive.
For example, if you have y= -3 + (-3), then the -3 in parenthesis is being multiplied by a positive 1, and would actually become y= -3 -3, which equals -6. But if you have y=-3 - (-3), you are multiplying the -3 by a negative 1, and would become y= -3 + 3, which would equal 0. Remember that if you have a - -, it becomes a + (I like to pretend to draw a line between the two - -'s to form a + sign to help you remember). If you have a + -, or a - +, it will always turn to -.