Yes you can. Using ETL or Extract-Transform-Load methodology, you will extract data & structure from older database, compare it with newer database structure, transform your older database structure into newer one by generating differential SQL DDL script, and at the end you will load transformed script to newer database.
You need some SQL knowledge, a good database management tool for comparison and transformation, and a few hours. In this way, you need not to go through each version rather you can jump from v4.80 to v5.40 directly.