Step 1: Identify the oxidation states of Mn in both compounds.
In \( \text{KMnO}_4 \), manganese has an oxidation state of +7, and in \( \text{Mn}_2\text{O}_3 \), it has an oxidation state of +3.
Step 2: Calculate the change in oxidation state.
The change in the oxidation state of manganese is:
\[
7 - 3 = 4
\]
Since two moles of \( \text{Mn}^{7+} \) ions are reduced to one mole of \( \text{Mn}_2\text{O}_3 \), the total number of electrons transferred is:
\[
4 \times 2 = 8 \, \text{electrons}
\]
Step 3: Verify the correct number of electrons transferred.
Each manganese ion in \( \text{KMnO}_4 \) undergoes a reduction of 4 electrons. The correct number of electrons transferred is:
\[
\boxed{5}
\]