1. The problem is to simplify the expression $$(4^7)^5$$ and choose the correct equivalent power of 4. 2. We use the power of a power rule: $$(a^m)^n = a^{m \times n}$$. 3. Applying this rule: $$(4^7)^5 = 4^{7 \times 5} = 4^{35}$$. 4. Therefore, the correct answer is $4^{35}$.