jargos, am glad to have you as a happy Linux Mint 17.2 user, and it shows the usefulness of not only the Linux OS, also of the computers that it's installed upon. There's no way of knowing other than it's certain, there's likely many more PC's & notebooks packed away in the closet for years, some may need a CMOS or notebook battery, otherwise are plenty for a Linux Mint install. While there's uncertainty whether or not the next or last LTS Ubuntu release (what Mint is built on) is the one that will be the last for 32 bit users (reports suggests the next is the last), yet that's OK, if it's the last LTS version, 14.04, one's supported until April 2019, if it's the next, then April 2021, chances are your computer won't outlive the last date w/out some major overhauling.
Yet that's still lots of time remaining, Ubuntu 16.04 (what Linux Mint 18 will be built on), will provide 5 more years of support & be better than the last & so will Linux Mint 18.
Any PC that has PAE instructions in the CPU can run a modern Linux system, regardless of age, and better yet, since the OS lacks the overhead of Windows, of course it'll run faster than some modern i5's, not all, yet some. It all depends on what one's doing. For general web browsing, extracting a file here & there, a P4 is perfectly fine for a Linux install. While onboard graphics will not be as good as Intel HD graphics or that of an addon card, some PC's does have a slot for a card, and if PCIe rather than PCI only, the more low cost & powerful options.
Today's mainstream GPU's uses a fraction of the power as old gen ones does, if the motherboard does have a PCIe connection, it's likely that either a nVidia 750 Ti variant or even the GTX 950 will install, yet to be honest, AMD has the edge over nVidia when it comes to drop in Linux compatibility w/out a lot of configuration & there's cards in the $100-125 (or less) range that will do the job nicely. Some may require a 6 pin power adapter, of which an adapter for 2 molex to one 6 pin adapter are often included, and others simply runs off of the power of the MB.
I've never used a PCI graphics card, so can't tell you nor anyone else to go from there.
Am very happy to have you here & look forward to more of you Linux postings. Should you have any further questions, please ask. There's no such thing as a 'dumb' question on our forum, other than the one not asked when in need. As a community we & assist & learn from one another, sharing & exchanging ideas, that's the way a proper Linux community operates.
Furthermore, now you no longer have to deal with the limitations of partitioning, as I recall, was a setback in another Topic. That PC in the closet freed you from the slavery of Windows, and as you said yourself, the more you use Linux Mint, the more you'll want to use it. I have 3 Windows installs on this PC & most of the time, rather than boot into one of those, will boot into the 40GiB Linux Mint 17.2 partition, my /home partition is on a HDD (a 1TiB sized HDD that was halved, half for Mint /home & the other, Windows Data) the majority of the time. With the resources that I have, don't have to, as Mint typically when Web browsing uses only 1-3% of the CPU & maybe 5% of the RAM, compared to 25% CPU & 25-30% of RAM on Windows.
That's the oddest issue with Windows, the more resources one dedicates to it, the more it'll use, and Windows 10 made things worse than better. First off, the Ethernet activity light is like a Christmas tree, always being used & glowing on a notebook, and if the Device Manager were opened, one would see the increased usage over Windows 7, 8 or 8.1. That's because it's uploading like mad as much data about You as possible. Also, that's what makes Cortana more effective, the more she knows about you, the better she can help. The heck with that, Google has been my personal digital assistant for a long time, and with adblockers in place, don't need to give away my soul for a OS.
I always maintained that Windows 10 wasn't going to be free, a catch to the deal. If one places a value on their privacy, grabbing a copy for $100 or so & use a Local account only is the best option. This can also be done with the more expensive Pro version, which also offers encryption via Bitlocker, yet that's only as good as how the computer is secured, if there's a place for a padlock, use it.
Fortunately with Linux Mint 17.2, one doesn't need to be worried over these things, just enjoy the computer to the max & be happy that you found a new life for it.
All the Best,