The numerator is
#x^2-16=(x-4)(x+4)#
The denominator is
#x^2-4x-5=(x-5)(x+1)#
Let
#f(x)=((x-4)(x+4))/((x-5)(x+1))#
Let's build a sign chart
#color(white)(aaaa)##x##color(white)(aaaa)##-oo##color(white)(aaaaa)##-4##color(white)(aaaa)##-1##color(white)(aaaaa)##4##color(white)(aaaaa)##5##color(white)(aaaaaa)##+oo###
#color(white)(aaaa)##x+4##color(white)(aaaaa)##-##color(white)(aaa)##0##color(white)(aaa)##+##color(white)(aaa)##+##color(white)(aaaa)##+##color(white)(aaaa)##+###
#color(white)(aaaa)##x+1##color(white)(aaaaa)##-##color(white)(aaa)####color(white)(aaaa)##-##color(white)(a)##||##color(white)(a)##+##color(white)(aaaa)##+##color(white)(aaaa)##+#
#color(white)(aaaa)##x-4##color(white)(aaaaa)##-##color(white)(aaa)####color(white)(aaaa)##-##color(white)(a)####color(white)(aa)##-##color(white)(a)##0##color(white)(aa)##+##color(white)(aaaa)##+#
#color(white)(aaaa)##x-5##color(white)(aaaaa)##-##color(white)(aaa)####color(white)(aaaa)##-##color(white)(a)####color(white)(aa)##-##color(white)(a)####color(white)(aaa)##-##color(white)(a)##||##color(white)(aa)##+#
#color(white)(aaaa)##f(x)##color(white)(aaaaaa)##+##color(white)(aaa)##0##color(white)(aaa)##-##color(white)(a)##||##color(white)(a)##+##color(white)(a)##0##color(white)(aa)##-##color(white)(a)##||##color(white)(aa)##+#
graph{((x+4)(x-4))/((x-5)(x+1)) [-14.24, 14.23, -7.12, 7.12]}
Therefore,
#f(x)>=0# when #x in (-oo,-4] uu(-1,4] uu (5,+oo)#