Excellent question! I love oxidation state questions.
First, let's look at the K (potassium). In an ionic compound, the potassium's oxidation state is always +1.
Next, let's look at the chlorate , ClO−3. The charge on the polyatomic ion is −1. You may be asking yourself, how do I know its charge will be−1?
Since the entire compound KClO3 has a charge of 0 and the K will have a charge of +1, the ClO3 must balance the K's +1 in the form of −1 for a net charge of 0.
When oxygen is with another element that is less electronegative than it is, the charge on the oxygen is −2. There are 3 oxygen atoms in the chlorate ion, for a total of −6 charge on the total of the 3 oxygen atoms.
Thus, charge of Cl+(−6)=−1. That means that the charge on chlorine in potassium chlorate is +5.
