Given:
- A pipe can fill a cistern in 8 hours.
- After half the tank is filled, three more similar taps are opened.

To find:
- The total time taken to fill the cistern completely.

Let's solve this problem step by step:

1. Calculation of the rate at which the pipe fills the tank:
- The pipe can fill the tank in 8 hours.
- Therefore, the rate at which the pipe fills the tank = 1/8 tank per hour.

2. Calculation of the time taken to fill half the tank:
- Let's assume that the capacity of the tank is 'T'.
- The pipe fills the tank at a rate of 1/8 tank per hour.
- Therefore, it will take (1/8)T hours to fill the tank completely.
- Half the tank will be filled in (1/2) * (1/8)T = (1/16)T hours.

3. Calculation of the rate at which the four taps fill the tank:
- After half the tank is filled, three more similar taps are opened.
- Therefore, the total number of taps filling the tank becomes 1 + 3 = 4.
- As the taps are similar, each tap will fill the tank at the same rate as the initial pipe.
- Therefore, the rate at which the four taps fill the tank = 4 * (1/8) tank per hour.

4. Calculation of the time taken to fill the remaining half of the tank:
- The remaining half of the tank is already filled at a rate of 1/8 tank per hour.
- The four taps fill the tank at a rate of 4 * (1/8) tank per hour.
- Therefore, the combined rate at which the tank is filled = 1/8 + 4 * (1/8) = 1/2 tank per hour.
- It will take 1/(1/2) = 2 hours to fill the remaining half of the tank.

5. Calculation of the total time taken to fill the cistern completely:
- The time taken to fill the first half of the tank = (1/16)T hours.
- The time taken to fill the remaining half of the tank = 2 hours.
- Therefore, the total time taken to fill the cistern completely = (1/16)T + 2 hours.

Hence, the correct answer is option (c) 5 hours.