About a year ago, I had a similar problem with my iPod classic. I dropped it, and there was a pretty noticeable line of dead pixels. Each time I carried it in my backpack, the area of dead pixels expanded—most likely from the iPod bumping around against everything else in my bag.
I decided to change the display before it got worse. The display replacement procedure is relatively simple, but the trickiest part is actually getting the iPod open first. It's completely possible, but just know that some some prying tools (along with patience) are required.
Luckily for you, we have an iPod 5th Generation Display Replacement guide, and we are also currently selling the display itself!
We know you've got what it takes to get your new display up and running. Good luck!