It is easy to solve this by the principle of complement.
The total number of number-plates CONTAINING both O and 0 are:
5*5 ways to fill the first two positions, of which 4*4 picks won't have the letter O. So, 5*5 - 4*4 = 9 arrangements will have the letter O.
10*10*10*10 ways to fill rest four positions, of which 9*9*9*9 arrangements won't have the digit 0. So, 10000-6561= 3439 arrangements will have the digit 0.
So, 9 * 3439 arrangements will have both O and 0.
Hence 5*5*10*10*10*10 - 9 * 3439 = 219,049 arrangements will NOT CONTAIN both O and 0.