I was riding down a nice smooth bike path the other day (at speed), and there was a branch full of thorns about 10m ahead of me, straddling the path. I couldn't have gone around it. One of the thorns pieced my tire, and pricked a hole in my inner tube - which slowly deflated. I will replace the inner tube - but is it worth me buying a new tire because of a 5mm hole from a thorn? Will this hole expose my inner tube too much? Thanks
A thorn hole in an inner tube is totally patchable. A 50 cent patch is a lot cheaper than a new tube. Stop consumerism!
As for the hole, it depends if the inner tube pokes out or not. The get-home fix is to line or reinforce that area with something laid between the tube and tyre.
On one tyre I ended up adding a patch to the inside of the tyre, which worked well enough. It lined up against the matching patch on the tube.
Holes in tires can be "temporarily" repaired by applying an emergency tire boot (e.g., TB-2 Emergency Tire Boot) to the inside of the tire over the hole. These patches are stiffer than a regular inner tube patch (providing some structural integrity) and they should have a sticky compound on one side to help keep them in one place. They are also much cheaper than buying a new tire. Inner tube patches may not be stiff enough to support the break in the tire carcass, so I would recommend against taking this approach.
That all said, these are not intended as "permanent" fixes as they can fail under extended use if the tear in the tire carcass is too large. What is too large, well that depends on the conditions you ride under and tire pressures you use. That said, 5mm hole is pretty small. I have run a tire boot on a similarly sized hole in a tire for well over a year without any issues. That said, in the end this is a personal decision, and you monitor the tire to see if 1) the tire boot is holding and 2) the hole is getting any worse.
Finally as mentioned by Criggie, please consider patching the tube before replacing with a new tube. If you use classic glue on patches (not the glueless variety) these repairs can last years. If you need to replace, please consider recycling the old tube.