Step 1: Understanding the Concept:
The history of Indian astronomy is marked by several landmark texts. Knowing their approximate dates of composition is essential for understanding the evolution of mathematical methods.
Step 2: Chronological Data:
1. Aryabhatiya (D): Composed by Aryabhata I in 499 CE. This is the earliest text in this list.
2. Panchasiddhantika (C): Compiled by Varahamihira around 505 CE. It summarizes five older Siddhantas.
3. Brahmasphutasiddhanta (A): Written by Brahmagupta in 628 CE. It corrected and expanded upon the older systems.
4. Khandakhadyaka (E): Also written by Brahmagupta, around 665 CE. It is a 'Karana' text based on Aryabhata's school.
5. Trishatika (B): Written by Sridharacharya, usually dated between the 8th and 9th centuries CE (approx. 750–850 CE).
Step 3: Final Sequence:
D (Aryabhatiya) $\rightarrow$ C (Panchasiddhantika) $\rightarrow$ A (Brahmasphutasiddhanta) $\rightarrow$ E (Khandakhadyaka) $\rightarrow$ B (Trishatika).
Step 4: Final Answer:
The correct chronological order is D, C, A, E, B.