Josanna's test scores to date are $90, 80, 70, 60,$ and $85.$ Her goal is to raise her test average at least $3$ points with her next test. What is the minimum test score she would need to accomplish this goal?
$\textbf{(A)}\ 80 \qquad \textbf{(B)}\ 82 \qquad \textbf{(C)}\ 85 \qquad \textbf{(D)}\ 90 \qquad \textbf{(E)}\ 95$
Take the average of her current test scores, which is
\[\frac{90+80+70+60+85}{5} = \frac{385}{5} = 77\]
This means that she wants her test average after the sixth test to be $80.$ Let $x$ be the score that Josanna receives on her sixth test. Thus, our equation is
\[\frac{90+80+70+60+85+x}{6} = 80\]
\[385+x = 480\]
\[x = \boxed{95 \textbf{(E)}}\]