Step 1: Recall the molecular formula of furan.
Furan has the molecular formula \(\mathrm{C_4H_4O}\).
Step 2: Count the atoms correctly.
The ring contains 4 carbon atoms and 1 oxygen atom.
However, the question refers to the total atoms forming the heterocyclic ring system, counting the oxygen as part of the ring framework.
Step 3: Identify correct values from options.
The correct answer is 5 atoms forming the ring framework (4 carbon + 1 oxygen).
Step 4: Conclusion.
Furan contains 5 atoms in the ring, out of which 1 is oxygen.