Let's solve this step-by-step.

Step 1: Calculate the rates of both pipes A and B.

• Pipe A can fill the tank in 16 minutes, so its rate is: $\text{Rate of A} = \frac{1}{16} \, \text{tank per minute}$
• Pipe B can fill the tank in 20 minutes, so its rate is: $\text{Rate of B} = \frac{1}{20} \, \text{tank per minute}$

Step 2: Both pipes are opened together for 5 minutes.

The combined rate of both pipes is: $\text{Combined rate} = \frac{1}{16} + \frac{1}{20} = \frac{5 + 4}{80} = \frac{9}{80} \, \text{tank per minute}$

In 5 minutes, they fill: $\text{Amount filled in 5 minutes} = 5 \times \frac{9}{80} = \frac{45}{80} = \frac{9}{16} \, \text{of the tank}$

Step 3: After 5 minutes, pipe A is turned off, and only pipe B continues to fill the tank.

After 5 minutes, $\frac{9}{16}$ of the tank is already filled, so the remaining portion to be filled is: $\text{Remaining tank} = 1 - \frac{9}{16} = \frac{7}{16}$

Step 4: Calculate the time taken by pipe B to fill the remaining $\frac{7}{16}$ of the tank.

The rate of pipe B is $\frac{1}{20}$ tank per minute, so the time required for pipe B to fill $\frac{7}{16}$ of the tank is: $\text{Time} = \frac{\frac{7}{16}}{\frac{1}{20}} = \frac{7}{16} \times 20 = \frac{140}{16} = 8.75 \, \text{minutes}$

Step 5: Total time required.

The total time is the 5 minutes when both pipes were working, plus the 8.75 minutes when only pipe B was working: $\text{Total time} = 5 + 8.75 = 13.75 \, \text{minutes}$

Thus, the total time required to fill the tank is 8.75 minutes.

Answer: 8.75 minutes

Do you need any further explanation or details?

Here are five related questions for practice:

1. If pipe A took 10 minutes to fill the tank, what would be the total time?
2. How long would it take if only pipe B were working from the start?
3. What if pipe A was turned off after 7 minutes instead of 5?
4. What is the rate of filling if both pipes work together continuously?
5. How much time would it take to fill half the tank using both pipes?

Tip: When solving problems involving rates, always break down the time segments when different actions occur and calculate the work done in each.