Final answer:
In the reaction, iron (Fe²⁺) acts as the reducing agent as it loses electrons and its oxidation state increases, while manganese in MnO₄⁻ acts as the oxidizing agent as it gains electrons and its oxidation state decreases.
Step-by-step explanation:
To identify the reducing agent and the oxidizing agent in the reaction 5Fe²⁺ + 8H⁺ + MnO₄⁻ → 5Fe³⁺ + Mn²⁺ + 4H₂O, we break down the reaction into half-reactions. We can see that iron (Fe²⁺) is oxidized to iron (Fe³⁺), showing an increase in oxidation state from +2 to +3, which means it loses electrons and therefore, is the reducing agent. On the other hand, manganese in MnO₄⁻ is reduced to Mn²⁺, as it undergoes a decrease in oxidation state from +7 to +2, indicating a gain of electrons and making it the oxidizing agent.