In a reaction:

\(MnO_4^- + 8H^+ + 5e^- \longrightarrow \underline{A} + H_2O\)

\(A\) stands for:

\(Mn^{2+}\)

The correct answer is option 3. \(Mn^{2+}\).

To determine the oxidation state (\(A\)) of manganese (\(Mn\)) in the reaction:

\[MnO_4^- + 8H^+ + 5e^- \longrightarrow A + H_2O\]

We can use the following rules:

In permanganate (\(MnO_4^-\)), manganese is in the +7 oxidation state (\(+7\)).

In the product (\(A\)), manganese will undergo a reduction, gaining electrons.

Given that \(MnO_4^-\) is reduced to \(A\), the oxidation state of manganese in \(A\) should be less than +7. The only option that satisfies this criterion is: 3. \(Mn^{2+}\)