Detective/Retardation

And here is the main question - how did those two 5k bills end up in his hands?

That' same not the main question. The main question is how to make sure this doesn't happen again.

The human brain is a mysterious and not even the most reliable thing. For example, I constantly double-check mine with gadgets. In your case, video surveillance would have helped, but since there isn't any, so be it.

The good news is that this also happens to professional cashiers. But rarely. Still, it happens. And that is why money disbursement rituals exist.
Count the money twice, moving it from your hands to the table or from one hand to another. If the amount is the same both times - give it to the recipient.
And of course, you should also count the money when receiving it.

The bad news is that such lapses don't just happen for no reason. Either you didn't get enough sleep (which you said yourself), or stress (moving, new environment), or problems with your head. I'm not ruling out the guy, of course, but those options turn out to be too fantastic. Sleep more, rest more, sign up for yoga or swimming. If it keeps happening - find a good psychiatrist and get checked.

By the way. This guy is showing how it's done. I've seen many different ways of counting money, but these are the best (though in the second one, I arrange bills in stacks of 10 rather than into a general pile).