Ok our equation is now : |x+3|+|x-2|= 5

And examining the following 4 cases we have:

1) which is accepted

2)

3)

4) and since x+3<0 => x<-3 ,for x=-3 we have -3<-3

Hence the solutions of the equation are:

x=2 or 5=5 or -5=5 or -3<-3 .And since we have :

x=2 or 5=5.

And the question is how do we get rid of 5=5