If you're given:
$$a \times b = (2, -4, 2),\quad a \times c = (7, 13, -11),\quad b \times c = (1, 7, 1)$$
what properties of cross products or formulas can you use to solve $(2b - c) \times (3a + 5c)$?
I want to utilize how there is a $c$ common to both vector arithmetics but I am not sure how.
Just break it into pieces, using $a\times(b+c)=a\times b+a\times c$.
What do you know that relates $a\times b$ with $b\times a$?