Explanation:

- Let's observe the pattern in the series: 5, 12, 31, 68, 129.

- The first term is 5.

- The second term is 12, which is 5 + 7.

- The third term is 31, which is 12 + 19.

- The fourth term is 68, which is 31 + 37.

- The fifth term is 129, which is 68 + 61.

- We notice the differences: 7, 19, 37, 61. These numbers seem to be consecutive prime numbers squared: \(7 = 2^2 + 3^2\), \(19 = 3^2 + 4^2\), \(37 = 5^2 + 6^2\), \(61 = 7^2 + 8^2\).

Now, let's predict the next difference using the pattern \(n^2 + (n+1)^2\).

- The next two squares are \(9^2 + 10^2 = 81 + 100 = 181\).

- Therefore, the next number is 129 + 101 = 220.

- Correct Option: 220