In any number, the last digit can be 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
We want that the last digit in the product is an odd digit other than 5,
i.e., it is any one of the digits 1, 3, 7, 9. This means that the product is not divisible by 2 or 5.
The probability that a number  is divisible by 2 or 5 is $\frac{6}{10}$.
[∵ In that case the last digit can be one of 0,2,4,5,6,8]

∴ The probability that the number  is not divisible by 2 or 5 $=1-\frac{6}{10}-\frac{4}{10}=\frac{2}{5}$
In order that the product is not divisible by 2 or 5,
none of tthe constituent numbers should be divisible by 2 or 5 and its probability $={\left(\frac{2}{5}\right)}^4=\frac{16}{625}$