5. Every day in November, Winnie-the-Pooh visited either Piglet, or Rabbit, or Eeyore. For any two consecutive days, he visited Piglet at least once, and for any three consecutive days, he visited Rabbit at least once. How many times could he have visited Eeyore during this time? (November has 30 days. Winnie-the-Pooh visited Eeyore at least once).
5. Suppose Winnie-the-Pooh visited Eeyore on some day in November, but not on the 1st or the 30th. Since over any two consecutive days he visited Piglet at least once, he must have visited Piglet the day before visiting Eeyore, and he must also have visited Piglet the day after visiting Eeyore. This means that over these three consecutive days, he did not visit Rabbit at all, which contradicts the condition. Therefore, Winnie-the-Pooh could visit Eeyore no more than twice (only on the 1st and the 30th of November). We will show that he could visit Eeyore once or twice. Let visits to Rabbit be denoted by K, to Piglet by P, and to Eeyore by I.

He could visit Eeyore once in the following way: IPKPK...PKP. He could visit Eeyore twice in the following way: IPKPPP...PKPKP...PKPI.