We calculate the first supersymmetric and kappa-symmetric derivative deformation of the M5-brane worldvolume theory in a flat eleven-dimensional background. By applying cohomological techniques we obtain a deformation of the standard constraint of the superembedding formalism. The first possible deformation of the constraint and hence the equations of motion arises at cubic order in fields and fourth order in a fundamental length scale l. The deformation is unique up to this order. In

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... this rules out any induced Einstein-Hilbert terms on the worldvolume. We explicitly calculate corrections to the equations of motion for the tensor gauge supermultiplet.