The first row of transition metals is Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn. The d shell holds 10 electrons, which are filled sequentially. That is:
Sc has 1 unpaired electron
Ti has 2 unpaired electrons
V has 3 unpaired electrons
Cr has 4 unpaired electrons
Mn has 5 unpaired electrons
Fe has 1 set of paired electrons and 4 unpaired electrons
Co has 2 sets of paired electrons and 3 unpaired electrons
…and so on until the d shell is filled with Zn (5 sets of paired electrons)
Therefore, your answer is Mn, with 5 unpaired electrons.
First Row Transition Metals
Joe is wrong. Although they do fill sequentially most of the time the electron configuration for Cr is [Ar] 4s1 3d5 not [Ar] 4s2 3d4 like expected. Therefore, Cr has the most unpaired electrons of the transition metal series with 6 unpaired electrons.