Answer
$75,287,520$
Work Step by Step
Using $_nC_r=\dfrac{n!}{r!(n-r)!},$ the given expression, $
_{100}C_{5}
,$ evaluates to
\begin{array}{l}\require{cancel}
=\dfrac{100!}{5!(100-5)!}
\\\\=
\dfrac{100!}{5!95!}
\\\\=
\dfrac{100(99)(98)(97)(96)(95!)}{5(4)(3)(2)(1)(95!)}
\\\\=
\dfrac{\cancel{100}^5(\cancel{99}^{33})(\cancel{98}^{49})(97)(96)(\cancel{95!})}{\cancel{5(4)}(\cancel{3})(\cancel{2})(1)(\cancel{95!})}
\\\\=
\dfrac{75287520}{1}
\\\\=
75,287,520
\end{array}