If three electrons are available to fill five empty 3d atomic orbitals, how will the electrons be distributed in the five orbitals?

Answer is: one electron in the first three orbitals, none in the fourth or fifth orbitals.  All three electrons will have parallel spins (unpaired electrons).
This is Hund's rule - orbitals of the same energy are each filled with one electron before filling any with a second, these first electrons have the same spin. 

Order of filling levels and sublevels of electrons: 1s²2s²2p⁶3s²3p⁶4s²3d¹⁰4p⁶5s²4d¹⁰5p⁶6s²3f¹⁴5d¹⁰6p⁶for an element with 5 electrons in the 3d energy level: full configuration: 1s²2s²2p⁶3s²3p³.