To form a committee of 2 girls and 3 boys from 5 girls and 7 boys:

Step 1: Combinations for Girls = \(^5C_2\) = \(\frac{5!}{(5-2)!2!}\) = 10

Step 2: Calculate the Combinations for Boys = \(^7C_3\) =  \(\frac{7!}{(7-3)!3!}\) = 35

the total number of ways to form the committee, multiply the combinations of girls and boys:  10 x 35 = 350ways

The total number of ways to form the committee is: 350.