What is the units digit of 3 to the 2004th power times 5 to the 2004th power?
[3^2004 * 5^2004] mod 10^10 ==5087890625 - these are the last 10 digits.
Note that \(3^{2004} \times 5^{2004} = 15^{2004}\)
Because the base ends in a 5, the ones digit will always be \(\color{brown}\boxed{5}\)