To solve the given puzzle, letâ€™s look for a pattern in the given equations:

1. 1 + 4 = 5

2. 2 + 5 = 12

3. 3 + 6 = 21

One way to look at it is by examining the relationship between the sum and the result. Notice:

1. 1 + 4 = 5

2. 5 + 2 + 5 = 12

3. 12 + 3 + 6 = 21

It seems that each equation is taking the result of the previous equation and adding the sum of the current numbers. Letâ€™s apply this to the final equation:

â€¢ Previous result: 21

â€¢ Current numbers: 5 and 8

So, 21 + 5 + 8 = 34

Therefore, 5 + 8 = 34.