1. **State the problem:** Find the value of $w$ such that $$(8^3 \times 8^4)^5 = 8^w.$$\n\n2. **Use the property of exponents for multiplication:** When multiplying powers with the same base, add the exponents: $$8^3 \times 8^4 = 8^{3+4} = 8^7.$$\n\n3. **Apply the power to a power rule:** $(a^m)^n = a^{m \times n}$, so: $$(8^7)^5 = 8^{7 \times 5} = 8^{35}.$$\n\n4. **Compare the resulting expression:** We have $8^{35} = 8^w$ which means $$w = 35.$$\n\n**Final answer:** $w = 35$.