Predict the next three numbers in the pattern

5,9,14,23,37,60,

The three next numbers would be: 97, 157, and 254

You would add first 2 number infront if the number wanted to be solved. For example numbers 5 and 9 in the pattern would make 14 (also in the pattern).

Add 37 and 60 to get 97, then add 60 and 97 to then get 157. Lastly add 97 to 157 to get 254.