The reduction of MnO$_4^-$ to MnO$_2$ involves a change in the oxidation state of Mn from +7 to +2.
According to the balanced redox reaction, the number of electrons required to reduce 1 mole of MnO$_4^-$ is 5.
Thus, the total charge required for the reduction is 5 Faradays (F).
Hence, the correct option is (3) 5 F.