Divisibility comparison between factorials

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).

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