1. **State the problem:** Solve the polynomial equation $$(5x - 2)^3 + 28 = 0$$ algebraically for the exact value of $x$. 2. **Rewrite the equation:** Move 28 to the right side: $$ (5x - 2)^3 = -28 $$ 3. **Take the cube root of both sides:** $$ 5x - 2 = \sqrt[3]{-28} $$ 4. **Isolate $x$:** $$ 5x = 2 + \sqrt[3]{-28} $$ 5. **Divide both sides by 5:** $$ x = \frac{2 + \sqrt[3]{-28}}{5} $$ 6. **Check the options:** The correct exact solution matches $$ x = \frac{2 + \sqrt[3]{-28}}{5} $$ **Final answer:** $$ x = \frac{2 + \sqrt[3]{-28}}{5} $$