7*3+3=24

7*4+1=29

so it would seem that

x$y=7x+y

if this is the case then we get

5$4=7*5+4=35+4=39

of course the issue with these kind of problems is that there are an infinite number of functions F(x,y) with which to define x$y such that the initial conditions are met.  Furthermore, for any given value Z we can find an F(x,y) such that the initial conditions are met and 5$4=Z so in that sense any answer is technically a valid answer.