Question 75856
There are two conditinos for equations containing absolute values
Condition #1
x-5=8 [because x could be greater than 0 (a positive number)]
x=8+5 [solve for x]
x=13
.
Condition #2
x-5=-8 [because x could be less than zero (a negative number]
x=-8+5 [solve for x]
x=-3
.
So the set is 
x such that x is {13 or -3}
.
Check by plugging either solution back into the original equation and solve.