For what value of n,

We need to find the value of $n$, for which $2^{n} \times 5^{n}$ ends in 5 .

Clearly,

$2^{n} \times 5^{n}=(2 \times 5)^{n}$

$=10^{n}$

Also, all the values of $n$ will make $10^{n}$ end in 0 .

Thus, there is no value of $n$ for which $2^{n} \times 5^{n}$ ends in 5 .