5. How many numbers of the form $\overline{a b a b a b}$, where $a$ and $b$ are different digits and $a \neq 0$, are divisible by 217?
5. $\overline{\mathrm{ababab}}=10101 \cdot \overline{\mathrm{ab}}=7 \cdot 1443 \cdot \overline{\mathrm{ab}}$, and $217=7 \cdot 31$. Since the number 31 is prime, and the number 1443 is not divisible by it. Therefore, the number $\overline{\text { ababab }}$ is divisible by 217 if and only if the number $\overline{\mathrm{ab}}$ is divisible by 31, that is, when $\overline{\mathrm{ab}}$ is 31, 62, and 93.