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For no value of n 2n∗5n ends in digit 5. The number 2n∗5n=(2∗5)n=10n and thus is a 1 followed by n zeros. Among the products 2n∗5m with two possibly different exponents for 2 and 5 the last digit equals 5 if and only if n=0 and m>0, so if it is a pure power of 5.
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