1. Rewrite the expression:

• We know that $32 = 2^5$, so: $32^5 = (2^5)^5 = 2^{25}$ Thus, the expression becomes: $32^5 + 2^{27} = 2^{25} + 2^{27}$

2. Factor out the common term:

• Factor $2^{25}$ from both terms: $2^{25} + 2^{27} = 2^{25}(1 + 2^2) = 2^{25}(1 + 4) = 2^{25} \times 5$

3. Divisibility Check:

• The expression is $2^{25} \times 5$.
• Divisibility by 3: $2^{25} \times 5$ is not divisible by 3, as it doesn't contain a factor of 3.
• Divisibility by 7: $2^{25} \times 5$ is not divisible by 7, as it doesn't contain a factor of 7.
• Divisibility by 10: $2^{25} \times 5$ is divisible by 10, because it contains both 2 and 5 as factors.
• Divisibility by 11: $2^{25} \times 5$ is not divisible by 11, as it doesn't contain a factor of 11.

Conclusion: The expression $32^5 + 2^{27}$ is divisible by 10. Correct Answer: C. 10