Russian used to have dual pronouns too, but they all were lost somewhere in the 13th century, as in all other Slavic languages other than Slovenian.

The system used for small numbers is probably a broad extension of an earlier dual number for nouns, i.e. something like a plural but just for two things. For (some) male nouns, the nominative dual ending was the same as the genitive singular, which was then extended to all other nouns even when this correspondence didn't hold, and from just 2 things to 3 and 4 as well. Nowadays the dual has been completely forgotten for nouns, and the only interpretation of the rule is that it's a genitive singular.

Whereas modern English only distinguishes grammatical number by singular/plural (and Old English had dual), some languages even have trial (three).

Russian distinguishes paucal (few) from plural (many). It’s not super common but there are some other languages that do it.

It’s not just 5, it’s also 21 to 25, 31 to 35 etc. However, some Slavic languages (e.g. Slovak and Czech) don’t do that, and only have those special numerals for under 5.