Series Analysis:
To find the missing term and complete the series, let's analyze the given series of numbers step by step.

Step 1:
The series starts with the number 5.

Step 2:
The next number is obtained by adding 7 to the previous number, i.e., 5 + 7 = 12.

Step 3:
The next number is obtained by subtracting 5 from the previous number, i.e., 12 - 5 = 7.

Step 4:
The next number is obtained by adding 8 to the previous number, i.e., 7 + 8 = 15.

Step 5:
The next number is obtained by subtracting 7 from the previous number, i.e., 15 - 7 = 8.

Step 6:
The next number is obtained by adding 10 to the previous number, i.e., 8 + 10 = 18.

Step 7:
The next number is obtained by subtracting 8 from the previous number, i.e., 18 - 8 = 10.

Step 8:
Based on the pattern observed in the given series, the next number can be obtained by adding 12 to the previous number, i.e., 10 + 12 = 22.

Therefore, the missing term in the series is 22.

Alternative Approach:
Alternatively, we can observe that the series alternates between adding and subtracting numbers.

- The first number is followed by an addition of 7.
- The second number is followed by a subtraction of 5.
- The third number is followed by an addition of 8.
- The fourth number is followed by a subtraction of 7.
- The fifth number is followed by an addition of 10.
- The sixth number is followed by a subtraction of 8.

Following this pattern, the next number in the series will be obtained by adding 12.

Therefore, the missing term in the series is 10 + 12 = 22.

Conclusion:
Based on the analysis, the missing term in the series is 22. Therefore, option C, 21, is the correct answer.