Answer
$-4 i-2j +5k$
Work Step by Step
Let us consider $P_1$ and $P_2$ as vectors and, a vector $\overrightarrow{P_1P_2}$ can be found as:
$\overrightarrow{P_1P_2}=\overrightarrow{P_2}-\overrightarrow{P_1}=\lt 1,2,0 \gt -\lt -3,0,5 \gt =\lt -4,-2,5 \gt$
Hence, our final answers is: $\overrightarrow{P_1P_2}=-4 i-2j +5k$