Paul has two jobs, working at a restaurant and tutoring at his school. Paul earns $\mathrm{\$}14$ an hour working at the restaurant and $22 an hour while tutoring. On a given week Paul must work no more than 20 total hours but must earn no less than 250 total dollars. If Paul works 5 hours at the restaurant, which of the following is an appropriate number of hours spent tutoring?
6 hours
17 hours
0 hours
20 hours
12 hours

Step 1 ：Paul earns $14 an hour at the restaurant and has already worked 5 hours. So, he has already earned $14\times 5=70$ dollars.

Step 2 ：He needs to earn at least $250 in total, so he still needs to earn $250-70=180$ dollars.

Step 3 ：He earns $22 an hour tutoring, so he needs to work $180÷22=8.18$ hours. However, he can't work a fraction of an hour, so he needs to work at least 9 hours.

Step 4 ：He has already worked 5 hours at the restaurant, so he can work up to $20-5=15$ hours tutoring.

Step 5 ：Therefore, the appropriate number of hours spent tutoring is between 9 and 15 hours. The only option in this range is 12 hours.

Step 6 ：Final Answer: The appropriate number of hours Paul should spend tutoring is $\boxed{{\displaystyle 12}}$ hours.