Let's do the long division
#color(white)(aaaa)##x^4+3x^3##color(white)(aaaaaaaa)##28x+15##color(white)(aaaa)##|##x+5#
#color(white)(aaaa)##x^4+5x^3##color(white)(aaaa)####color(white)(aaaaaaaaaaaaaaaa)##|##x^3-2x^2+10x-22#
#color(white)(aaaaa)##0-2x^3#
#color(white)(aaaaaaa)##-2x^3-10x^2#
#color(white)(aaaaaaaaa)##-0+10x^2+28x#
#color(white)(aaaaaaaaaaaaa)##+10x^2+50x#
#color(white)(aaaaaaaaaaaaaaaa)##+0-22x+15#
#color(white)(aaaaaaaaaaaaaaaaaaaa)##-22x-110#
#color(white)(aaaaaaaaaaaaaaaaaaaaaa)##+0+125#
Therefore,
#(x^4+3x^3+28x+15)/(x+5)=(x^3-2x^2+10x-22)+125/(x+5)#