Answer
$10$
Work Step by Step
RECALL:
${n}\choose{k}$$=\dfrac{n!}{k!(n-k)!}$
Use the formula above to obtain:
${5}\choose{3}$$\require{cancel}=\dfrac{5!}{3!(5-3)!}=\dfrac{5!}{3!2!}=\dfrac{5\cdot 4\cdot 3 \cdot 2 \cdot 1}{(3\cdot 2 \cdot 1) (2 \cdot 1)}=\dfrac{5\cdot \cancel{4}^2\cdot \cancel{3 \cdot 2 \cdot 1}}{(\cancel{3\cdot 2 \cdot 1}) (\cancel{2} \cdot 1)}=10$