
Yes, it does mean 5 rubles and specifically a paper bill. A coin ( 5 kopeek) would be пятачок or пятак.
IMHO, you could have looked for an English equivalent for пятеркa, because it is not a universally recognized word transliterated,
as opposed to Troika. Troika with horses is totally off because there's no troika w/out horses. Troika of horses would be fine.
I don't think ( could be wrong) that carriages with horses are "driven". Even if they are "let's drive" sounds off to me. Only one person
drives so in my book it either "Drive!" or "Let's go!"
Do you need help with the meaning of "ножки бьешь"? I don't think you can find it in a dictionary
домой пойдешь is you'll go home
домой пpидешь is you'll come home
Писем море написала more means "a lot" ( as in "as many as the sea is big )
* 5-ruble note. Translated as "last fiver" per suggestions in the comments
** Carriage with three horses
*** Phrase basically meaning a lot of letters (see comments)