\((x-3)^3+2^2\cdot5=-7\\\Rightarrow (x-3)^3+4\cdot5=-7\\\Rightarrow(x-3)^3+20=-7\\\Rightarrow(x-3)^3=-7-20\\\Rightarrow(x-3)^3=-27\\\Rightarrow(x-3)^3=(-3)^3\\\Rightarrow x-3=-3\\\Rightarrow x=-3+3=0\)
\(\left(x-3\right)^3=-7-20=-27\Leftrightarrow\left(x-3\right)^3=\left(-3\right)^3\)
\(\Leftrightarrow x-3=-3\Leftrightarrow x=0\)