jmc

If there are $5$ people, we can arrange then in $5\cdot 4\cdot 3=60$ ways. Since we don't care about order, we've overcounted. There are $3\cdot 2\cdot 1=6$ ways to arrange $3$ people, so our answer is $$\frac{60}{6}=\boxed{10}.$$Alternatively, the number of groups of three that five people can make (without regard to the order the groups) is $\left(\genfrac{}{}{0ex}{}{5}{3}\right)=\frac{5!}{3!2!}=\boxed{10}$.