An international group of zookeepers with successful breeding programs made the following animal exchanges last year. Using the same bartering system, how many oryxes can a zoo obtain in exchange for $15$ flamingos?

$\backslash$table$[[3$ oryxes $=1$ tiger,$2$ flamingos $=1$ anteater$],[1$ camel $=6$ anteaters,$5$ lemurs $=1$ rhino$],[1$ rhino $=4$ monkeys,$3$ lemurs $=1$ camel$],[3$ monkeys $=1$ tiger,$1$ rhino $=4$ oryxes$]]$