Sofia ran $5$ laps around the $400$-meter track at her school. For each lap, she ran the first $100$ meters at an average speed of $4$ meters per second and the remaining $300$ meters at an average speed of $5$ meters per second. How much time did Sofia take running the $5$ laps? 
$\qquad\textbf{(A)}\ \text{5 minutes and 35 seconds}$ 
$\qquad\textbf{(B)}\ \text{6 minutes and 40 seconds}$ 
$\qquad\textbf{(C)}\ \text{7 minutes and 5 seconds}$ 
$\qquad\textbf{(D)}\ \text{7 minutes and 25 seconds}$ 
$\qquad\textbf{(E)}\ \text{8 minutes and 10 seconds}$
If Sofia ran the first $100$ meters of each lap at $4$ meters per second and the remaining $300$ meters of each lap at $5$ meters per second, then she took $\frac{100}{4}+\frac{300}{5}=25+60=85$ seconds for each lap. Because she ran $5$ laps, she took a total of $5 \cdot 85=425$ seconds, or $7$ minutes and $5$ seconds. The answer is $\boxed{\textbf{(C)}\ \text{7 minutes and 5 seconds}}$.