Answer
$$[x]_S=\left[ \begin {array}{ccc} -6\\ 12\\ -4\\ 9\\-8\end {array} \right].$$
Work Step by Step
Since we have
$$x= -6(1,0,0,0,0)+12(0,1,0,0,0)-4(0,0,1,0,0)+9(0,0,0,1,0)-8(0,0,0,0,1),$$
then the coordinate matrix of $x$ in $R^5$ relative to the
standard basis is
$$[x]_S=\left[ \begin {array}{ccc} -6\\ 12\\ -4\\ 9\\-8\end {array} \right].$$