#### Answer

$x=-1,\pm2,5$

#### Work Step by Step

Step 1. As $5$ is a solution of the equation, we use synthetic division as shown in the figure.
Thus, we have
$(x-5)(x^3+x^2-4x-4)=0$
Step 2. Factor the second term as
$x^3+x^2-4x-4=x^2(x+1)-4(x+1)=(x+1)(x^2-4)=(x+1)(x+2)(x-2)$
We have the equation as
$(x-5)(x+1)(x+2)(x-2)=0$
Step 3. We can identify the solutions as
$x=-1,\pm2,5$