Expand the expression $(1-2x)^{5}$.

Using the Binomial Theorem,the expansion of $(a+b)^{n}$ is given by $\sum_{k=0}^{n} {n \choose k} a^{n-k} b^{k}$.
For the expression $(1-2x)^{5}$,we have $a=1$,$b=-2x$,and $n=5$.
$(1-2x)^{5} = {5 \choose 0}(1)^{5} + {5 \choose 1}(1)^{4}(-2x) + {5 \choose 2}(1)^{3}(-2x)^{2} + {5 \choose 3}(1)^{2}(-2x)^{3} + {5 \choose 4}(1)^{1}(-2x)^{4} + {5 \choose 5}(-2x)^{5}$
$= 1(1) + 5(-2x) + 10(4x^{2}) + 10(-8x^{3}) + 5(16x^{4}) + 1(-32x^{5})$
$= 1 - 10x + 40x^{2} - 80x^{3} + 80x^{4} - 32x^{5}$