x+y-5=xy-7
=>x+y-xy=-2
=>x-xy+y=-2
=>\(x\left(1-y\right)+y-1=-3\)
=>\(-x\left(y-1\right)+\left(y-1\right)=-3\)
=>(-x+1)(y-1)=-3
=>(x-1)(y-1)=3
=>\(\left(x-1;y-1\right)\in\left\{\left(1;3\right);\left(3;1\right);\left(-1;-3\right);\left(-3;-1\right)\right\}\)
=>\(\left(x;y\right)\in\left\{\left(2;4\right);\left(4;2\right);\left(0;-2\right);\left(-2;0\right)\right\}\)