  We present "M5 algebra" to derive Courant brackets of the generalized
geometry of $T\oplus \Lambda^2T^\ast \oplus \Lambda^5T^\ast$: The Courant
bracket generates the generalized diffeomorphism including gauge
transformations of three and six form gauge fields. The Dirac bracket between
selfdual gauge fields on a M5-brane gives a $C^{[3]}$-twisted contribution to
the Courant brackets. For M-theory compactified on a five dimensional torus the
U-duality symmetry is SO(5,5) and the M5 algebra basis is in the 16-dimensional
spinor representation. The M5 worldvolume diffeomorphism constraints can be
written as bilinear forms of the basis and transform as a SO(5,5) vector. We
also present an extended space spanned by the 16-dimensional coordinates with
section conditions determined from the M5 worldvolume diffeomorphism
constraints.
