Which of the following would logically be next in the sequence: A5I, D7J, G9K, ....?

Mapping the alphameric values, we can see that the numeric position of the alphabets give an average which is the same as the number between the two:

A+I= (1+9)/2 = 5

D+J = (4+10)/2 = 7

G+K = (7+11)/2 = 9

The next term in the series should also be following this pattern. 

Also looking at the series we can see that the numbers ae increasing by 2 each turn, the next term should have 11 in the middle. 

This narrows down options to C and E. 

Of the two options, D would give an average of (11+13)/2 = 12

Hence E is the most logical next term of the series.