Balancing the redox reaction involves ensuring the number of atoms and the charges are equal on both sides.
The oxidation state of manganese in \( \text{MnO}_4^- \) is +7, and it is reduced to +2 in \( \text{Mn}^{2+} \).
The number of electrons transferred is 5.
Similarly, the oxalate ion \( \text{C}_2\text{O}_4^{2-} \) is oxidized to \( \text{CO}_2 \), requiring 4 protons (\( \text{H}^+ \)) to balance the equation.
Thus, the correct coefficients for \( \text{C}_2\text{O}_4^{2-} \) and \( \text{H}^+ \) are 5 and 4, respectively.