Let f₅(n) be the largest integer x for which 5^x divides n.
For example, f₅(625000) = 7.

Let T₅(n) be the number of integers i which satisfy f₅((2·i-1)!) < 2·f₅(i!) and 1 ≤ i ≤ n.
It can be verified that T₅(10³) = 68 and T₅(10⁹) = 2408210.

Find T₅(10¹⁸).