Answer
$118,755$ different committees.
Work Step by Step
The order in which the members are selected does not matter and no member can be selected more than once.
Combination of 29 distinct members taken 5 at a time:
$_{29}C_5=\frac{29!}{5!(29-5)!}=\frac{29!}{5!\times24!}$
But, $29!=29\times28\times27\times26\times25\times(24\times23\times22\times...\times3\times2\times1)=29\times28\times27\times26\times25\times24!$
$_{29}C_5=\frac{29\times28\times27\times26\times25\times24!}{5!\times24!}=\frac{29\times28\times27\times26\times25}{5\times4\times3\times2\times1}=\frac{14,250,600}{120}=118,755$
