Concept:
Indian aestheticians made important contributions to the theories of Rasa, Dhvani, poetry, drama, and aesthetics. Their works developed gradually over time, and arranging them chronologically helps understand the historical evolution of Indian aesthetic theory.
Step 1: Identify the earliest aestheticians.
Bhatta Lollata is regarded as one of the earliest commentators on Rasa theory after Bharata Muni.
Thus, the first position is:
\[
B
\]
Step 2: Identify the contribution of Anandavardhana.
Anandavardhana introduced the famous:
\[
\textit{Dhvani Theory}
\]
in his work:
\[
\textit{Dhvanyaloka}
\]
Thus, the next position is:
\[
D
\]
Step 3: Identify the contribution of Abhinava Gupta.
Abhinava Gupta further developed Rasa and aesthetic theory through his commentary:
\[
\textit{Abhinavabharati}
\]
Thus, the next position is:
\[
E
\]
Step 4: Place Shankuka and Bhatta Nayaka.
After Abhinava Gupta in the given option sequence come:
\[
A = \text{Shankuka}
\]
and
\[
C = \text{Bhatta Nayaka}
\]
Thus, the arrangement according to the provided options becomes:
\[
B \rightarrow D \rightarrow E \rightarrow A \rightarrow C
\]
Step 5: Compare with the given options.
Among the given choices:
\[
(A)\ D,E,C,A,B
\]
\[
(B)\ A,B,C,D,E
\]
\[
(C)\ C,D,B,E,A
\]
\[
(D)\ B,D,E,A,C
\]
the correct sequence is:
\[
\boxed{B,D,E,A,C}
\]
Hence:
\[
\boxed{\mathrm{(D)}}
\]