How many pairs of integers (a,b) are necessary to make sure that for two of them, say $\displaystyle ({a_1},{b_1})$ and $\displaystyle ({a_2},{b_2})$ it is the case that $\displaystyle {a_1}$ mod 5 = $\displaystyle {a_2}$ mod 5 and $\displaystyle {b_1}$ mod 5 = $\displaystyle {b_2}$ mod 5?