Concept:
Vijayanagara period mural paintings are connected with temple and palace art of South India.
Important sites of Vijayanagara murals include Hampi and Lepakshi.
Step 1: Check Hampi.
Hampi was the capital region of the Vijayanagara Empire.
It contains important monuments and mural traditions related to the Vijayanagara period.
So:
\[
C = \text{Correct}
\]
Step 2: Check Lepakshi.
Lepakshi is famous for Vijayanagara period paintings.
The murals at Lepakshi are very important examples of South Indian mural painting.
So:
\[
E = \text{Correct}
\]
Step 3: Eliminate other options.
Ellora and Bagh are earlier cave and mural traditions.
Badami is connected with Chalukyan art, not the Vijayanagara mural tradition in this question.
Step 4: Final conclusion.
Vijayanagara period murals are found at:
\[
C,\ E
\]
Hence:
\[
\boxed{\text{(C) C and E only}}
\]