Russian 5 Ruble Advance Card

Ha Ha and three times Ha.
There's no such place as Zabaykalsn; it's a (slight) abbreviation in the first place, and you still managed to misspell it!
The actual translation is, approximately, "Trans-Baykalian Mountain Consumer's Cooperative" (Baykal being a very large and deep lake, indeed fairly close to the Chinese-Russian border). I googled, and apparently it was actually located in Chita (coincidentally since 2008 the capital of Zabaykalsky Krai - i.e. Trans-Baykalian District).
For the record, yes, the rest of your post (i.e. the non-quoted part) seems to be, at least approximately, true

Thank you both so much. We have some old paper money from between 1914 and 1921. The research has been really fun. The money traces the steps of a families travels to the United states. Some of it is even worth a good amount of money.

Thanks again

It would be very difficult, my guess would be its rare but also low in value just because of how obscure it is. Check out any catalogs that specialise in the Russian Civil War, not standard catalog will have these nor will a website.