[tex]f(x)=3x-7\\\\g(x)=x^2-4\\\\(f-g)(x)=f(x)-g(x)\\\\Therefore\\\\(f-g)(-5)=f(-5)-g(-5)\\\\Put\ the\ value\ of\ x=-5\ to\ the\ equation\ of\ the\ function\ f\\and\ to\ the\ equation\ of\ the\ function\ g:\\\\f(-5)=3(-5)-7=-15-7=-22\\\\g(-5)=(-5)^2-4=25-4=21\\\\(f-g)(-5)=-22-21=-43\to\boxed{C.}[/tex]
