what are the charge and coordination number of the central transition metal ion(s) in each compound below?

The coordination number is simply the number of complex bonds to the central atom, and only involves the complex ion itself. The oxidation number is the charge it would have if all bonds were ionic, and involves the ligands and also the ions not bound in the complex ion itself.

For K[Pt(NH3)Cl5], the coordination number for Pt is 6, because there are 6 ligands on the Pt atom. The oxidation number must be calculated, however. K is +1, so the complex ion must be -1 overall. Therefore, Pt + NH3 + 5Cl = -1. Cl is -1 and NH3 is 0, so Pt + 0 + 5(-1) = -1, so Pt = -1 + 5 = +4. Thus, oxidation state of Pt is +4 and coordination number is 6.

For [Pt(en)2Br2](ClO4)2, the coordination number is again 6. Ethylenediamine forms 2 coordinate bonds per en ligand, and bromine forms 1, so 2(2) + 2(1) = 4+2 = 6. Oxidation number is again +4, since en is neutral, and Br and ClO4 are both -1, so their total contribution is -4 and must be balanced by the +4 on the Pt.

The last one is tricky, since both ions are complexes. Of the ligands, only Cl is charged, whereas en and NH3 are not. The total amount of charge from the ligands, therefore, is 4(-1) = -4. The central metal ions must sum to +4. So there are possible combinations involving 0 and +4, +1 and +3, or +2 and +2. Copper can be either +1 or +2 in compounds, whereas cobalt is more usually +2 than +3, so the combination +2 and +2 seems most appropriate. Now for coordination numbers, Cu has 4 bonds to it (2 from the en and 2 from the NH3), so its coordination number is 4. Co has 6 bonds to it, so its coordination number is 6. Therefore: Cu oxidation state +2, coordination number 4, and Co oxidation state +2, coordination number 6.

K[Pt(NH3)Cl5]

Potassium ion has a single positive charge, K+, therefore the complex itself must have a single negative charge for the compound to be neutral. Ammonia, NH3, is a neutral ligand so does not contribute to charge. Chloride has a single negative charge, Cl-, therefore Pt must be +4 oxidation state to give a 1- charge on the complex. The coordination number is 6 because it is surrounded by 6 ligands so there are 6 coordinate bonds.

[Pt(en)2Br2](ClO4)2

ClO4- has a single negative charge so the complex itself has a 2+ charge. En, ethylenediamine, is a neutral bidentate ligand, so doesn't contribute to charge. Bromide has a single negative charge, Br-, so Pt must again have a +4 oxidation state. Because en is bidentate it binds twice to the transition metal therefore there coordination number is again 6.

For the last part I'm not sure I understand the question however if X is representing a halide then:

[Cu(en)(NH3)2]X

Cu must be +1 oxidation state and the coordination number is 4.

X[Co(en)Cl4]

Co must be +5 oxidation state and coordination number 6.

Hope this helps!