From the above people saying a 5600G would make it a gaming PC is not really true it would absolutely sux for any modern game and most older games.
It depends where you draw the line. It can run a
lot of games, but that won't mean anything if it doesn't include the games
you want.
In the build i suggested i left room for a GPU, hence the 750w PSU. For $500 or under, there is not a snowball's chance in hell of getting good gaming performance, esp. modern demanding games. That needs a $1000-1500 budget at least, not including monitor.
But you can sink hundreds of hours into RimWorld, Hard West, Sins, Factorio or 4X games, to name a few. Throw in classics like KOTOR and Jade Empire, or the original Vampire The Masquerade Bloodlines and probably dozens of games i forgot, not to mention indie games.
All of them can run on the iGPU. + Win11 and other conveniences of a modern OS.
It's a lot of PC for the money. To get more you need another $300-600 for a new GPU. And here we do agree. For the kind of modern performance in modern games, that kind of GPU is required. But it won't go into a machine like the one OP has. Even if power wasn't a consideration, there is only so much a 3570 can do in 2024.