\(\left[x\right]_U=\left(x;y;z\right)^T\)
\(\Rightarrow\left(4;-3;4\right)=x\left(-2;-1;-2\right)+y\left(-2;-2;-3\right)+z\left(-1;5;5\right)\)
\(\Rightarrow\left\{{}\begin{matrix}-2x-2y-z=4\\-x-2y+5z=-3\\-2x-3y+5z=4\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}x=-67\\y=60\\z=10\end{matrix}\right.\)
\(\Rightarrow\left[x\right]_U=\left(-67;60;10\right)^T\)