This volume contains a collection of papers presented at the Fifth International Conference on Fibonacci Numbers and their Applications. The topics covered include number patterns, linear recurrences, and the application of the Fibonacci Numbers to probability, statistics, differential equations, cryptography, computer science and elementary number theory. Many of the papers included contain suggestions for other avenues of research. The contents of this volume attest to a growing interest in, and importance of, the pure and applied aspects of Fibonacci Numbers in many different areas of science of engineering. The proceedings of the four previously held conferences have also been published by Kluwer. For those interested in application of number theory, statistics and probability, and numerical analysis in science and engineering.