Will Linux Mint Run Smoothly on My Old i7 Setup?

That sounds like a solid build! I'm running Pop!_OS on a similar setup, and it works great. Mint will probably be awesome for you as well!

You should be all set! Most Ubuntu-based distros should run without any hiccups. Your GPU will support the NVidia drivers for a bit longer, but if you're just casual gaming, you could always switch to the open-source Nouveau drivers. If you can, adding more RAM and an SSD will definitely make everything feel smoother, but your current specs are good for editing 1080p video and such.

Just give it a shot! What I find acceptable might differ from others, but with your specs, you should be just fine.

Your computer’s still in good shape. You might not even need Mint; if you're after something a bit flashier, you can handle that too. The performance drop in Windows isn’t really tied to your hardware degrading, so you'll find plenty of options for any desktop-oriented distro out there.

I’ve got Mint Cinnamon running on laptops with just 4GB of RAM, and they perform really well. You should have no issues with your setup—it’s definitely capable!