$${ \left(x-5 \right) }^{ 2 } =2(x-3)+(x+2)(x-2)-1$$
$x=3$
$$x^{2}-10x+25=2\left(x-3\right)+\left(x+2\right)\left(x-2\right)-1$$
$$x^{2}-10x+25=2x-6+\left(x+2\right)\left(x-2\right)-1$$
$$x^{2}-10x+25=2x-6+x^{2}-4-1$$
$$x^{2}-10x+25=2x-10+x^{2}-1$$
$$x^{2}-10x+25=2x-11+x^{2}$$
$$x^{2}-10x+25-2x=-11+x^{2}$$
$$x^{2}-12x+25=-11+x^{2}$$
$$x^{2}-12x+25-x^{2}=-11$$
$$-12x+25=-11$$
$$-12x=-11-25$$
$$-12x=-36$$
$$x=\frac{-36}{-12}$$
$$x=3$$
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