We present M5 algebra to derive Courant brackets of the generalized geometry of $Toplus Lambda^2T^ast oplus Lambda^5T^ast$: 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.
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