solution: Probability questions are sometimes answered by calculating the ways the event will NOT happen, then subtracting.  In this problem the $1$, $2$, $3$, $4$ and $6$ faces are paired to create $5 \times 5 = 25$ number pairs whose product is NOT multiples of 5.  This leaves $36 - 25 = 11$ ways to get a multiple of $5$, so the probability is $\boxed{\frac{11}{36}}$.
prompt.content: <|im_start|>system
  You are a helpful assistant.<|im_end|>
  <|im_start|>user
  Two fair, 6-sided dice are thrown.  What is the probability that the product of the two numbers is a multiple of 5?  Express your answer as a common fraction.
  Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
  <|im_start|>assistant
  
prompt.role: user
extra_info.answer: \frac{11}{36}
extra_info.question: Two fair, 6-sided dice are thrown.  What is the probability that the product of the two numbers is a multiple of 5?  Express your answer as a common fraction.
extra_info.split: test