Summary: A D-5-brane bound state with a self-dual field strength on a 4-torus is considered. In a particular case this model reproduces the D5-D1 brane bound state usually used in the string theory description of 5-dimensional black holes. In the limit where the brane dynamics decouples from the bulk the Higgs and Coulomb branches of the theory on the brane decouple. Contrasting with the usual instanton moduli space approximation to the problem the Higgs branch describes fundamental excitations of the gauge field on the brane. Upon reduction to 2-dimensions it is associated with the so-called instanton strings. Using the Born-Infeld action for the D-5-brane we determine the coupling of these strings to a minimally coupled scalar in the black hole background. The supergravity calculation of the cross section is found to agree with the D-brane absorption probability rate calculation. We consider the near horizon geometry of our black hole and elaborate on the corresponding duality with the Higgs branch of the gauge theory in the large \(N\) limit. A heuristic argument for the scaling of the effective string tension is given.