I think those are different questions with different answers.
10s: as OG says, it's to do with the decimal system; we just think in 10s. Even more so in hundreds (think cricketers); and 25 and 50 are subsections of that.
You could say that 5 is halfway to 10, in the same fashion. I'm not sure 5 really is a big anniversary, though.
21 was I think traditionally the age of adulthood, when you could drink, vote and so on. This isn't generally true any longer but the tradition lingers on. Exactly why it's 21 rather than 22, I couldn't tell you, though.