jmc

Let the number of questions Frank answered correctly be $a$ and the number of questions he answered incorrectly be $b$. We have the two equations $$\begin{array}{rl}a+b& =80\\ 5a-2b& =232\end{array}$$ From the first equation, we have $b=80-a$. Substituting this into the second equation to eliminate $b$, we have $5a-2(80-a)=232\Rightarrow a=56$. Thus, Frank answered $\boxed{56}$ questions correctly.