$.....\Leftrightarrow x^{5}+y^{5}-x^{4}y-xy^{4}\geq 0\Leftrightarrow x^{4}(x-y)-y^{4}(x-y)\geq 0$$\Leftrightarrow (x-y)(x^{4}-y^{4})\geq 0\Leftrightarrow (x-y)^{2}(x+y)(x^{2}+y^{2})\geq 0$(luôn đúng)$\Rightarrow ĐPCM$
$.....\Leftrightarrow x^{5}+y^{5}-x^{4}y-xy^{4}\geq 0\Leftrightarrow x^{4}(x-y)-y^{4}(x-y)\geq 0$$\Leftrightarrow (x-y)(x^{4}-y^{4})\geq 0\Leftrightarrow (x-y)^{2}(x+y)(x^{2}+y^{2})\geq 0$(luôn đúng)
$.....\Leftrightarrow x^{5}+y^{5}-x^{4}y-xy^{4}\geq 0\Leftrightarrow x^{4}(x-y)-y^{4}(x-y)\geq 0$$\Leftrightarrow (x-y)(x^{4}-y^{4})\geq 0\Leftrightarrow (x-y)^{2}(x+y)(x^{2}+y^{2})\geq 0$(luôn đúng)
$\Rightarrow ĐPCM$