We are given that,

A matrix has 5 elements.

We need to find all the possible orders.

We know that if there is a matrix A, of order m × n.

Then, there are mn elements.

Or,

If a matrix has mn elements, then

The order of the matrix = m × n or n × m

For example,

If a matrix is of order 1 × 2, then

There are 2 elements in the matrix.

Or,

If a matrix is of order 2 × 1, then

There are 2 elements in the matrix.

Similarly,

If a matrix has 5 elements, then

The order of this matrix are 1 × 5 or 5 × 1.

Thus, possible orders of a matrix having 5 elements are 1 × 5 and 5 × 1.