  We propose a complete Born-Infeld-like action for a bosonic 5-brane with the
worldvolume chiral field in a background of gravitational and antisymmetric
gauge fields of D=11 supergravity. When the five-brane couples to a three-rank
antisymmetric gauge field local worldvolume symmetries of the five-brane
require the addition to the action of an appropriate Wess-Zumino term. To
preserve general coordinate and Lorentz invariance of the model we introduce a
single auxiliary scalar field. The auxiliary field can be eliminated by gauge
fixing a corresponding local symmetry at the price of the loss of manifest d=6
worldvolume covariance. The double dimensional reduction of the five-brane
model results in the Born-Infeld action with the Wess-Zumino term for a D=10
four-D-brane.
