Find all $x,y\in\mathbb{Z}^+$ such that $y^2(x-1)=x^5-1$

Question

Find all $x,y\in\mathbb{Z}^+$ such that $y^2(x-1)=x^5-1$

$y^2=x^4+x^3+x^2+x+1\Rightarrow (y+1)(y-1)=x(x^3+x^2+x+1)$

if $x=2k\Rightarrow y=2t+1$

if $y=2k\Rightarrow x=2t+1$

if $x=1\Rightarrow y$ can be anything

if $y=1\Rightarrow x=1$

now we should find all $x,y>1$

i tried some other things too but they did not went well

can you give me hint?...