In particular, the author illustrates the discrete quintic spline interpolation involving forward differences and the periodic discrete quintic spline interpolation involving central differences. The book I Progress on Difference Equations and Discrete Dynamical Systems i contains selected contributions from the 25th International Conference on Difference Equations and Applications (ICDEA 2019) which was held at UCL (University College London) from June 24-28, 2019. Progress on difference equations and discrete dynamical systems: edited by Steve Baigent, Martin Bohner, and Saber Elaydi, 25th ICDEA, London, UK, June 24-28, 2019, Springer Nature Switzerland AG, 2020, 448 pp., EUR 139.99, ISBN 978-3-030-60106-5. [Extracted from the article]