A boy needs to select five courses from 12 available courses, out of which 5 courses are language courses.…

Case I -

When $0$ language course is selected from $5$ particular language courses, then total number of ways

$={}^{7}C_5=21$

Case II -

When $1$ language course is selected from $5$ particular language courses, then total number of ways

$={}^{7}C_4{}^{5}C_1=175$

Case III -

When $2$ language course is selected from $5$ particular language courses, then total number of ways

$={}^{7}C_3{}^{5}C_2=350$

So, required ways$=546$