1. **State the problem:** Simplify the expression $$(2a^4 + 5)^2$$. 2. **Formula used:** To square a binomial, use the formula $$(x + y)^2 = x^2 + 2xy + y^2$$. 3. **Apply the formula:** Here, $x = 2a^4$ and $y = 5$. 4. **Calculate each term:** - $x^2 = (2a^4)^2 = 4a^8$ - $2xy = 2 \times 2a^4 \times 5 = 20a^4$ - $y^2 = 5^2 = 25$ 5. **Combine all terms:** $$ (2a^4 + 5)^2 = 4a^8 + 20a^4 + 25 $$ 6. **Final answer:** $$\boxed{4a^8 + 20a^4 + 25}$$