Each n-by-n matrix with n>1 is a sum of 5 coninvolutory matrices

An $ntimes n$ complex matrix $A$ is called coninvolutory if $bar AA=I_n$ and skew-coninvolutory if $bar AA=-I_n$ (which implies that $n$ is even). We prove that each matrix of size $ntimes n$ with $n>1$ is a sum of 5 coninvolutory matrices and each matrix of size $2mtimes 2m$ is a sum of 5 skew-coninvolutory matrices. We also prove that each square complex matrix is a sum of a coninvolutory matrix and a condiagonalizable matrix. A matrix $M$ is called condiagonalizable if $M=bar S^{-1}DS$ in which $S$ is nonsingular and $D$ is diagonal.