My answer:
AI,CL,DP,GR,KS
Solution:
Convert the letters to numbers 1-9,3-12,4-16,X-X,X-X = A-I,C-L,D-P,x-x,x-x as you can see by adding the value of the letters we get:\begin{align*}9+1&=10\\ 12+3&=15\\16+4&=20,\end{align*}that is, a sequence that increases by five every time: $10,15,20,25,30$.
Notice also that the sequence made of first letters has a leapfrog pattern: $$\text{A, C, D}=1,3,4; 1+3=4,$$so the next two initial letters should be $4+3=7$ and $7+4=11$.
Therefore, our final sequence is $\boxed{\text{AI, CL, DP, GR, KS}}$ , where x-x,x-x is $7-18, 11-19=\text{GR},\text{KS}$.