In the context of a five-dimensional brane-world model motivated from heterotic M-theory, we develop a framework for potential-driven brane-world inflation. Specifically this involves a classification of the various background solutions of (A)dS5 type, an analysis of five-dimensional slow-roll conditions and a study of how a transition to the flat vacuum state can be realized. It is shown that solutions with bulk potential and both brane potentials positive exist but are always non-separating...