5. (10 points) Among the divisors of a four-digit palindrome, exactly 3 are prime, and 39 are not prime. The value of the four-digit palindrome is


6336
【Solution】According to the rule that the sum of the digits in the odd and even positions of a double palindrome is equal, it must be a multiple of 11, and the number of factors is $3+39=42$. A four-digit number contains 3 prime numbers, so 42 needs to be decomposed into the product of 3 numbers. $42=2 \times 3 \times 7$.

Therefore, the double palindrome can be written as $a \times b^{2} \times c^{6}$. Let's see what the smallest case is when the prime numbers are the smallest. $11 \times 3^{2} \times 2^{6}$ $=6336$.

When the prime numbers are a bit larger, such as $b=5$ and $c=2$, $11 \times 5^{2} \times 2^{6}=17600$ (which does not meet the condition of being a four-digit number). Therefore, the answer is: 6336.