Step 1: Understanding the Concept:
Tracking the tenure of the Governors of the Reserve Bank of India (RBI) is important to understand the history of monetary policy reforms in India.
Step 2: Detailed Explanation:
Let us list the exact service periods for the specified RBI Governors:
1. M. Narasimham (D): Served as the 13th Governor of RBI from 2nd May 1977 to 30th November 1977.
2. Dr. Manmohan Singh (B): Served as the 15th Governor of RBI from 16th September 1982 to 14th January 1985.
3. Dr. C. Rangarajan (C): Served as the 19th Governor of RBI from 22nd December 1992 to 21st November 1997.
4. Dr. D. Subba Rao (A): Served as the 22nd Governor of RBI from 5th September 2008 to 4th September 2013.
5. Shaktikanta Das (E): Assumed office as the 25th Governor of RBI on 12th December 2018 and is currently serving.
Thus, the correct chronological order from earliest to latest is D $\rightarrow$ B $\rightarrow$ C $\rightarrow$ A $\rightarrow$ E.
Step 3: Final Answer:
The chronological sequence is D, B, C, A, E, matching Option (C).