Let f(x)=(x^2+5x)/(x-3)=(x(x+5))/(x-3)
The domain of f(x) is D_(f(x))=RR-{3}
Let's do a sign chart to solve this inequality
color(white)(aaaa)xcolor(white)(aaaa)-oocolor(white)(aaaa)-5color(white)(aaaa)0color(white)(aaaa)3color(white)(aaaa)+oo
color(white)(aaaa)x+5color(white)(aaaaa)-color(white)(aaaa)+color(white)(aaa)+color(white)(aaa)+
color(white)(aaaa)xcolor(white)(aaaaaaaaa)-color(white)(aaaa)-color(white)(aa)+color(white)(aaa)+
color(white)(aaaa)x-3color(white)(aaaaa)-color(white)(aaaa)-color(white)(aaa)-color(white)(aaa)+
color(white)(aaaa)f(x)color(white)(aaaaaa)-color(white)(aaaa)+color(white)(aaa)-color(white)(aaa)+
Therefore f(x)>=0 when x in [-5,0 ] uu ]3, +oo[
graph{(x^2+5x)/(x-3) [-72.6, 75.47, -19.23, 54.86]}