The last digit is my target

As shown below, the last digit of n!n! for each of n=5,6,7n=5, 6, 7 is zero: 5!=120,6!=720,7!=5040.5!=12{\color{#D61F06}0},\quad 6!=72{\color{#D61F06}0},\quad 7!=504{\color{#D61F06}0}. Is it true that the last digit of n!n! is zero for all positive integers n>4?n>4?

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