As things stand, you'd need to unplug your speakers to use conventional headphones (with a 3.5mm jack). To avoid doing so, your easiest option would be to use a splitter, so that the sound output could be fed to both the (conventional) headphones and to the speakers. e.g. this:
https://tinyurl.com/b9jxap2p
If you were to follow such a route, I'd suggest ensuring that you purchased headphones with a built-in volume control. Otherwise you'd need to control the volume directly from the computer, which would also affect the speaker volume.
An alternative solution might be to add Bluetooth functionality to your computer by plugging an adapter into a spare USB port. e.g.
https://tinyurl.com/22thvb9h . You could then use Bluetooth headphones.
Irrespective of how you use speakers or headphones though, I'd suggest that a 14-year-old PC is almost certainly in need of replacing. It needn't cost much; I recently sourced a refurbished Windows 10 desktop PC for a friend (from an approved charity seller on eBay, with excellent customer reviews), with a fast processor, loads of RAM and a solid state drive for just £85 including carriage. I'd be prepared to bet that it works a great deal better than your current PC does!