An $n \times n$ pentadiagonal matrix (with $n\ge 3$ is a matrix of the form $$ \begin{pmatrix} c_1 & d_1 & e_1 & 0 & \cdots & \cdots & 0 \\ b_1 & c_2 & d_2 & e_2 & \ddots & & \vdots \\ a_1 & b_2 & \ddots & \ddots & \ddots & \ddots & \vdots \\ 0 & a_2 & \ddots & \ddots & \ddots & e_{n-3} & 0 \\ \vdots & \ddots & \ddots & \ddots & \ddots & d_{n-2} & e_{n-2} \\ \vdots & & \ddots & a_{n-3} & b_{n-2} & c_{n-1} & d_{n-1} \\ 0 & \cdots & \cdots & 0 & a_{n-2} & b_{n-1} & c_n \end{pmatrix}. $$ It follows that a pentadiagonal matrix is determined by five vectors: one $n$ vector $c=(c_1,\ldots, c_n)$ two $(n-1)$ vectors $b=(b_1,\ldots, b_{n-1})$ and $d=(d_1,\ldots, d_{n-1})$ and two $(n-2)$ vectors $a=(a_1,\ldots, a_{n-2})$ and $e=(e_1,\ldots, e_{n-2})$ It follows that a pentadiagonal matrix is completely determined by $n+2(n-1)+2(n-2)=5n-6$ scalars.