Answer
26 ordered pairs
Work Step by Step
a $mod$ 5 can take 5 values i.e {0,1,2,3,4}
So for the ordered pair (a,b) we have 5$\times$5 = 25 combinations {(0,1),(0,2)..(1,0)......(4,4)}
Hence by pigeonhole principle we can see that we need at least 26 ordered pairs ($a,b$).