Or vice versa...
Another old song, of Lithuanian origin (or East Polish or Baltic - all roughly the same area), is mentioned on some German-language and Italian-language sites, called in German "Zogen einst fünf wilde Schwäne" (five wild swans once went out), dating from the 17th-century, possibly the Thirty Years War, as being possibly an antecedent of the Jacobi poem. The last of the three verses mention five young men who went off to war, none of whom returned.
Zogen einst fünf wilde Schwäne,
Schwäne leuchtend weiß und schön.
Which brings to mind a poem, Le cinque anatre (the five ducks) by the present day Italian poet, Francesco Guccini.