To solve the problem, we first need to identify the pattern in the given series:

5, 10, 13, 26, 29, 58, 61, ?

Let's examine the differences between consecutive terms:

• 10 - 5 = 5
• 13 - 10 = 3
• 26 - 13 = 13
• 29 - 26 = 3
• 58 - 29 = 29
• 61 - 58 = 3

We can observe that terms alternate between adding a larger number and adding 3. The sequence of larger numbers increases in a specific pattern:

• 5, 13, 29

Notice how these numbers are related to doubling the next reference point:

• 5 doubles to form 10(indirectly, we just start from 5)
• 13 is related to doubling 5 + 3 (which doesn't immediately fit, but isn't used further)
• 29 is near double of 13, and so on

More accurately, every alternate operation doubles the previous increment except when derived in a reset fashion using the 3 additions in between:

• After adding 3 to even-out, follows a notable larger increment.

Following this pattern, after doubling previous major number 29, the series should arrive at:

• Double of 29 is 58
• 61 - 58 confirmed the last 3 after doubling a reference number.
• Hence, needed complement is double outside current known boundaries hence:
• Next increment using a larger number in similar progression doubles becomes 58 + 64 = 122

The missing term in the sequence is 122.