@oldturkey03 is our resident expert on old school iPods, but it looks to me like an issue with the polarizer. That means the fix will be to replace the screen. Here's the guide you'll need to make that repair.
[guide|612|iPod 5th Generation (Video) Display Replacement - iFixit Repair Guide|new_window=true]
The screen itself isn't particularly expensive; normally you can support iFixit's repair efforts by purchasing it right here on iFixit, but they appear to be out of stock at the moment.
[product|IF195-000|iPod Video Color Display|new_window=true]
You can also find them on the major sites like Amazon, eBay and AliExpress. Here's an example of a very inexpensive one on AliExpress, but you can easily find more if you want it faster.
[link|https://www.aliexpress.us/item/2261799922952941.html|Internal LCD Display Screen Repair Part for iPod 5th Video 30GB 60GB 80GB 6th 7th Classic 80GB 120GB Thick Thin 160GB - AliExpress|new_window=true]