Rank and solvability of a 3 by 5 system

Let $A$ be a $3\times 5$ matrix defined by $$A=\begin{pmatrix}0&1&3&1&2\ 1&6&2&3&4\ 1&8&8&5&8\end{pmatrix}.$$ Consider the system of linear equations given by $$A\begin{pmatrix}x_1\ x_2\ x_3\ x_4\ x_5\end{pmatrix}=\begin{pmatrix}3\ 1\ 10\end{pmatrix},$$ where $x_1,x_2,x_3,x_4,x_5$ are real variables. Then