$P$+$Q$=$(x²y+xy²-5x²y²+x³)+(3xy²-x²y+x²y²)$
=$x²y+xy²-5x²y²+x³+3xy²-x²y+x²y²$
=$(x²y-x²y)+ (xy²+3xy²)-(5x²y²-x²y²)+x³$
=$4xy²-4x²y²+x³$
$P$-$Q$=$(x²y+xy²-5x²y²+x³)-(3xy²-x²y+x²y²)$
=$x²y+xy²-5x²y²+x³-3xy²+x²y-x²y²$
=$(x²y+x²y)+(xy²-3xy²)-(5x²y²-x²y²)+x³$
=$2x²y-2xy²-6x²y²+x³$
$Q$-$P$=$(3xy²-x²y+x²y²)-(x²y+xy²-5x²y²+x³)$
=$3xy²-x²y+x²y²-x²y-xy²+5x²y²-x³$
=$(3xy²-xy²)-(x²y+x²y)+(x²y²+5x²y²)-x³$
=$2xy²-2x²y+6x²y²-x³$