Concept:
Different musicological texts mention different numbers of melas.
To solve this question, we arrange the texts according to the increasing number of melas described in them.
Step 1: Start with Raag-Vibodh.
Raag-Vibodh is placed first in the increasing order.
So:
\[
A = \text{Raag-Vibodh}
\]
Step 2: Next comes Swarmela Kalanidhi.
Swarmela Kalanidhi comes after Raag-Vibodh.
So:
\[
B = \text{Swarmela Kalanidhi}
\]
Step 3: Next comes Sadraag-Chandrodaya.
Sadraag-Chandrodaya is placed after Swarmela Kalanidhi.
So:
\[
C = \text{Sadraag-Chandrodaya}
\]
Step 4: Next comes Raag-Tarangini.
Raag-Tarangini comes after Sadraag-Chandrodaya.
So:
\[
D = \text{Raag-Tarangini}
\]
Step 5: Last comes Shree-Mallakshyasangeetam.
Shree-Mallakshyasangeetam is placed at the end of the increasing order.
So:
\[
E = \text{Shree-Mallakshyasangeetam}
\]
Step 6: Final arrangement.
Thus, the correct order is:
\[
A \rightarrow B \rightarrow C \rightarrow D \rightarrow E
\]
Hence:
\[
\boxed{\text{(A) A, B, C, D, E}}
\]