Step 1:
Rameshwaram is situated in Tamil Nadu and is the southernmost among the given places.
Step 2:
Tirupati lies in Andhra Pradesh, while Tryambakeshwara is in Maharashtra.
Step 3:
Omkareshwara is in Madhya Pradesh and Vaidyanathadhama lies further north.
Step 4:
Thus, from South to North:
\[
\boxed{B \rightarrow A \rightarrow C \rightarrow E \rightarrow D}
\]
Hence, the correct option is:
\[
\boxed{\text{(4)}}
\]