TurboTax is not going to store your information or keep track of it for 50+ years.
Here are some options.
1. If you have online access to your IRA account you might be able to download a PDF of the Form 5498. The web site might even have a history of contributions.
2. Scan the form and save the PDF.
3. Keep your own record of contributions in a spreadsheet. This would probably be the most useful format if you need the information decades from now.