On bilinear complexity of multiplication of $5\times2$ matrix by $2\times2$ matrix

In this paper we study bilinear complexity (i.e. the minimum number of multiplications without using commutativity of the elements) for the problem of multiplication of matrices of small size. We show that the bilinear complexity for the problem of multiplication of a $5\times2$ matrix by a $2\times~2$ matrix is at least 17 for any field.