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 #"KClO"_3# has a charge of #0# and the #"K"# will have a charge of #+1#, the #"ClO"_3# 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#.
