$\left.\begin{array}{c}7B\\ 5G\end{array}\right\}\to \left(\begin{array}{c}3B\\ 2G\end{array}\right)$

Total number of ways of forming a team of $3$ boys and $2$ girls $={}^7{C}_3\times {}^5{C}_2=\frac{7.6.5}{1.2.3}\times \frac{5.4}{1.2}=350$

Total number of ways of forming a team if two specific boys $B_1,B_2$ always join the team

$={}^5{C}_1\times {}^5{C}_2=50$

So, the total number of ways of forming a team so that two specific boys never come together

$=350-50=300$