#### Answer

{-17}.

#### Work Step by Step

x+5 = -12
Step 1: subtract 5 from both the sides
x+5-5= -12-5
Step 2: Simplify
x= -17
Now we check the proposed solution, -17, by replacing x with -17 in the original equation.
Step 1: the original equation x+5 =-12
Step2: Substitute -17 for x
-17 +5 = -12
Step 3: Solve -17+5= -12
-12 = -12
Since the check results in true statement, we conclude that the solution set of the given equation is {-17}.