Concept:
Entropy ($S$) is a state function, meaning its change depends only on initial and final states, not on the path.
Step 1: Identify paths: A → B → C and A → D → E → C represent different paths between same states.
Step 2: Since entropy is a state function, total change is independent of path taken.
Step 3: Hence, sum of entropy changes along both paths must be equal.
\[
\Delta S_1 + \Delta S_2 = \Delta S_4 + \Delta S_5 + \Delta S_3
\]
Conclusion:
The given relation is always true.