Every solution to $Px = 0$ is scalar multiple of $\begin{bmatrix} 2 & 5 & 4 &3 & 1 \end{bmatrix}^T$, It means out of 5 column vectors of matrix $P$, $4$ are linearly independent as we have only one line in NULL Space (along the given vector).
Rank is nothing but the number of linearly independent column vectors in a matrix which is $4$ here.