1. Stating the problem: We need to solve for $j$ in the equation $$\sqrt[3]{4j + 4} = 5$$. 2. To eliminate the cube root, cube both sides of the equation: $$\left(\sqrt[3]{4j + 4} \right)^3 = 5^3$$ which simplifies to $$4j + 4 = 125$$. 3. Next, isolate $j$ by subtracting 4 from both sides: $$4j = 125 - 4$$ $$4j = 121$$. 4. Finally, divide both sides by 4 to solve for $j$: $$j = \frac{121}{4}$$ 5. Therefore, the value of $j$ is $$\boxed{30.25}$$.