We construct BPS-exact solutions of the world-volume Born-Infeld plus WZW action of a D5-brane in the background of N D3-branes, The non-trivial background metric and RR five-form field strength play a crucial role in the solution, When a D5-brane is dragged across a stack of N D3-branes a bundle of N fundamental strings joining the two types of branes is created, as in the Hanany-Witten effect. Our solutions give a detailed description of this bundle in terms of a D5-brane wrapped on a sphere. We discuss extensions of these solutions which have an interpretation in terms of gauge theory multi-quark states via the AdS/CFT correspondence. (C) 1999 Elsevier Science B.V.