jmc

We can try to guess and check to find the answer. If she got five right, her score would be $(5\ast 5)-(5\ast 2)=15$. If she got six right her score would be $(6\ast 5)-(2\ast 4)=22$. That's close, but it's still not right! If she got 7 right, her score would be $(7\ast 5)-(2\ast 3)=29$. Thus, our answer is $\boxed{7}$.