I may be wrong, but I'm pretty sure my old Technics table used to have the same cartridge and I couldn't get original stylus replacements. There were plenty of pattern parts but I was never sure on their quality.
I think you have three options (once you've put the turntable on a decent surface of course). For £10-15 you could get a pattern stylus replacement but I doubt that would deliver much improvement.
Next in terms of cost you could get a replacement cartridge starting with something like an Audio Technica 95e for about £30 (probably the cartridge that would have come in the LP5, haven't checked) through to the Ortofon 2M range probably a red for around £80 or a blue for £150 ish. These need to be fitted, wired and setup so if you've never done it before it will make a great learning experience - plenty of stuff on the Internet and all the help you'll need on here.
Finally, for a bit more money, you can get something like an Ortofon plug and play headshell that comes with the cartridge already mounted in a new headshell and you just remove your existing and fit the new one. There will still be a bit of setup required in terms of counterweight and possibly anti-skate, but less than a new cartridge in your existing headshell.
If I was you and was dubious about spending money on an old table and the process of changing a cartridge (and of course I'm not you, so take this with a pinch of salt), I'd plump for the AT95e which is unbeleivably good for the money and take my time to learn all about changing and setting up cartridges. That way, you will probably learn a lot and if you decide later you should have got a better cart or changed the table you have only spent £30 which frankly you'd probably get back if you ebayed the Technics with the AT95 on it rather than the original cart!