Here it says how many valence electrons with a manganese 5 ion possess. So manganese 5 means it has A5 plus or +5 charge. That means that it has lost five electrons. So remember, manganese is a transition metal. It is in Group seven of the periodic table. Don't confuse group 7 with group 7A. Group 7A are the halogens, right? But here we're talking about group 7 for this manganese ion.
So here for manganese, when it's neutral, it has seven valence electrons, but it just lost five, so we're going to subtract out five. So it should have two valence electrons left. If you wanted to do it the longer way, through the use of the electron configuration, you could also do that O. Here we need to find out what the electron configuration is of the neutral manganese. It would be Argon 4S23D5.
Now remember, 5 means we would lose 5 electrons, and we lose them from the highest shell number first. So we'd lose to both of these electrons from 4S, so they'd be completely gone, and we need to lose 3 more to get to +5 charge. Those additional three would have to come from the 3D set of orbitals. So when we lose three more, we'd have left two electrons.
Remember, the number of valence electrons per transition metal is the s + d orbital electrons. We lost our 4S orbital electrons, so all we have left are these two D orbital electrons. So whether you do it the long way through the electron configuration, or if you just simply remember the secondary Grou number for the transition metals is equal to their valence electrons, you'd also find out that you have two valence electrons left. So choose the way that you're most comfortable with to get your final answer.