#### Answer

{-5}

#### Work Step by Step

5x = -25
Step 1: Divide both the sides by 5
$\frac{5x}{5}$ = $\frac{-25}{5}$
Step 2: Simplify
x= -5
Now we check the proposed solution, -5, by replacing x with -5 in the original equation.
Step 1: the original equation 5x =-25
Step2: Substitute -5 for x
5.(-5) = -25
Step 3: Solve 5.(-5)=-25
-25 =-25
Since the check results in true statement, we conclude that the solution set of the given equation is {-5}.