"Iodide anion I(-I)"Iodide anion I(-I) is OXIDIZED to elemental iodine.....
I^(-) rarr 1/2I_2 + e^(-)I−→12I2+e− (i)(i)
And "Iodate anion I(V+)"Iodate anion I(V+) is REDUCED to elemental iodine.....
IO_3^(-) +6H^(+) + 6e^(-) rarr I^(-) + 3H_2OIO−3+6H++6e−→I−+3H2O (ii)(ii)
We adds (i)(i) and (ii)(ii) so as to eliminate the electrons.......i.e. 6xx(i) +(ii):6×(i)+(ii):
IO_3^(-) +cancel(6)5I^(-) + 6H^(+) + cancel(6e^(-)) rarr cancel(I^(-)) + 3I_2 + 3H_2O+cancel(6e^-)
To give finally........
IO_3^(-) +5I^(-) + 6H^(+) rarr 3I_2 + 3H_2O
Mass and charge are balanced as is absolutely required. Please note that all I have done is to balance mass and charge according to the standard rules of oxidation; and you yourself can become very adept at this with practice. If there is an issue you want clarified, raise it, and someone will address your question.