Answer
$4.5\ min$
Work Step by Step
Step 1. The taps would fill $1/5$ of the sink per minute.
Step 2. The drain would empty $1/10$ of sink per minute.
Step 3. Together, they would fill $1/5-1/10=1/10$ of the sink per minute.
Step 4. After one minute, the sink would be $1-1/10=9/10$ empty.
Step 5. With the taps, it will take $5(\frac{9}{10})=4.5\ min$ more to fill the sink.