<|system|>
What is the smallest prime divisor of $5^{23} + 7^{17}$?</s>.
<|user|>
Can you answer based on context?
<|assistant|>
Since $5^{23}$ and $7^{17}$ are both odd, their sum is even and therefore divisible by 2.  There are no smaller primes than $2$, so it is the smallest prime divisor of the sum.