In episode 5 of Dance in the Vampire Bund, “Shadow of Vampire” (シャドウ オブ ヴァンパイア), Mina shows herself to be more than just a vampire with a lot of power by showing off her mathematical prowess. Her work in front of the class is not the cutting edge of mathematics, but it would be more than what the average modern person is capable of (sadly to say; I do think that everyone should be able to do something as basic as proving there are an infinite number of primes, although I’m also pretty sure that what was shown on the blackboard was either plain wrong or an overly roundabout way of doing it).
The same thing cannot be said for Mina’s cooking skills. She is a total klutz at cooking, despite her denials to the contrary. Yuki is really bothered by what the relationship between Mina and Akira might actually be, so she volunteers herself to help Mina out, using it as a chance to get to know her. Thanks to this, Mina manages to cook up some delicious food, despite their terrible appearance and her rather weak sense of taste. But later on, when Yuki tries to confront Mina about having a ring that Yuki had given to Akira, this pisses off Mina: we were previously shown how Yuki tried to pass off Akira’s ring as something she gave to him, but Mina knows where the ring really came from.
Mina then has to deal with the prime minister, who is very much set against the legislation that would grant special status to the Bund. He intends to take the incredibly drastic step of dissolving the Diet to stop the legislation. Despite the incredible economic harm that this will do to Japan, he thinks it will be remembered as his great legacy of repelling vampires from Japan. Mina has her own backup plan that involves kidnapping the prime minister’s grandson, but she doesn’t threaten it: she just does it.
Meanwhile, Akira is having troubles of his own at school. A lot of students are very unfriendly towards him due to his association with Mina, particularly after rumors are spread about how the school president was attacked by vampires. The credibility of the rumors are strong considering that they’re backed up by photographic evidence. Of course, despite vampires who were violently opposed to Mina Tepes being shown on television twice already, a lot of people still seem to think that vampires are just a single power bloc. Things seem even worse when the nefarious group of vampires mixed in with the students appear to be recruiting more members.
It’s a pain for Akira when these vampires attack him while he is with Yuki. Being reluctant to turn into a werewolf in front of Yuki, Akira has a hard time with the attacks, but by the time he has had enough, it turns out that the vampires were already tipped off that Akira is a werewolf, and he suffers from an attack with silver dust. Fortunately, Mei Ren shows up with her candy of doom to save Akira and Yuki, who manage to run away. Although it wouldn’t be impossible for Mei Ren to have set up the whole thing …
Considering that it was raining, the first thing that Akira and Yuki think to do after running away is obviously to take off all their clothes to dry them off. When Yuki hears from Akira how Mina sneaked away to meet him, she claims to have seen a lot of people following them for Mina’s protection. I have my doubts that Mina’s protectors would have been so easily visible to the average person, but even granting that Yuki may have saw them, I do doubt that they really were Mina’s protectors: they were likely to be observers or even protectors unknown to Mina that have their own agenda, which probably includes Mei Ren, and could turn against her at any time.
Of course, with Akira and Yuki both being naked at their age, it doesn’t take long before it occurs to them what else people tend to do while naked. That thought gets derailed when Mina makes a call to check up on Akira. After what Akira heard from Yuki, he asks Mina whether he can trust her. While Mina answers in the affirmative, she appears to be fully aware how a kidnapping might go down with Akira. While it won’t be going against Akira’s trust, no doubt she is aware how poorly the excuse of realpolitick would work with him.