ELI5: Why does closing eyes when tired feel good?
The biggest reason is because when your body starts to prepare for sleep, one of the things it does is it starts producing less tears. This is because it is expecting you to close your eyes and keep them closed for a while, so it shouldn't have to do as much work washing the eyes.
If you push past this and keep your eyes open and stay awake even when your body wants to sleep, your eyes tend to get dry and irritated. At which point closing them lubricates them up again and feels pretty damn good.
The other answers are better but here's one for a 5 year old:
whenever your body needs something, it makes you feel good when you do that thing as a reward! Dehydrated? Water tastes gooood! Super hungry? Just about any food tastes gooood. Time to poop or pee? Feels gooood (usually). Our bodies have evolved this way to make sure things that are necessary are rewarded. When your body needs sleep, it rewards you when you get into a comfortable sleeping position and close your eyes by making that feel goood.
I left out some of the other things that feel good because, well, you're 5.
I'm slightly late but simple evolution/survival advantage usually gives useful biology answers even if you don't know/want the precise mechanisms as others I'm sure will explain.
So closing your eyes/sleeping is useful to do when you're tired biologically sleeping, in the same way it's a good idea to be happy and slightly hungry imagining food/shelter, your body imagining/miming the first step of sleep, which is what it needs when you're tired, should encourage you to do it, it's that simple and for brain and behaviour stuff most things we do give a survival advantage of some kind, although somewhat geared towards a gatherer-hunter lifestyle which can backfire in modern life. Like how closing your eyes during work/school might be considered rude but wasn't so much 10K years ago.
Why does eating when youre hungry feel good or drinking when youre thirsty? Scratching an itch? Same reason. Brain signals/chemicals rewarding you for fulfilling urges.