Answer
$(-5,-\frac{5}{3},- \frac{5}{2})$
Work Step by Step
We know that $a(-1,0,0)+b(0,0,-3)+c(0,-2,0)=(5,5,5)$.
Thus $-a=5
\\ -2c=5\\
-3b=5$.
Thus $a=-5 \\ c= - \frac{5}{2} \\ b =-\frac{5}{3}$
Thus the vector is $(-5,-\frac{5}{3},- \frac{5}{2})$.