reconcile yearly credit card statements

You say that you have 5 years of records per client, but I don't think there is a need to go back that far. If you find a mistake 5 years back, the credit card company won't care. The error was carried forward into the current and fixing it would be too hard. The terms and conditions probably only give you a few months to address an error.

If theses clients are a business then their accountant or tax advisor should already have these records. They would have had to use these records not just to double check the numbers but also to perform the required business and tax calculations. Getting the records from an accounting tool into a spreadsheet is another question for another site.

If these clients want you to use the paper records, then you should bill them for the amount of time it takes. Many credit cards will allow you to download the records going back x months. Some may allow you to go back even farther, but they may charge you for these additional months, but even $10 a month would be cheaper then paying somebody to enter the items by hand.

For future months you should either download the records directly from a website, or require the client to provide the downloaded data in something besides a hard copy or pdf.