jmc

Let $a$ denote the number of questions Andy got wrong, $b$ the number of questions Beth missed, $c$ the number of questions Charlie answered incorrectly, and $d$ the number of questions Daniel got wrong. Using the information given in the problem, we can form the following system of linear equations: $$\begin{array}{rl}a+b& =c+d\\ a+d& =b+c+4\\ c=5& \end{array}$$ Adding the first two equations together yields $2a+b+d=2c+b+d+4$, which simplifies to $a=c+2$. Since $c=5$, Andy must have answered $\boxed{7}$ questions incorrectly.