This volume constitutes the refereed proceedings of the fifth Workshop on Algorithm Engineering, WAE 2001, held in Aarhus, Denmark, in August 2001. The 15 revised full papers presented were reviewed and selected from 25 submissions. Among the topics addressed are: implementation, experimental testing, and fine-tuning of discrete algorithms; novel use of discrete algorithms in other disciplines; empirical research on algorithms and data structures; and methodological issues regarding the process of converting user requirements into efficient algorithmic solutions and implementations.