Triumph 500s are fine bikes ... I have one which I ride ... a lot ... and I love it!
The speedo cable is an easy enough fix, provided the speedo drive is still good ... often, the cable is removed for a reason, though. In the worst case scenario, you'll need to pull the rear wheel to replace the drive box. However, that doesn't mean the speedo is gonna work. Those magnetic Smith's gauges have a pretty short life span. Rebuilt units are available and there are people who rebuild them ... there are also cheap knock-offs available (I see them on ebay all the time) that I've heard work just fine if you don't care about originality.
If you remove your tach drive and shine a light in there, you should be able to determine if your cam has the drive slot or not. The slot is a separate piece that you can add. If it does have the slot, reinstall the tach drive and tuen the motor ... if the output of the drive unit does not spin, you may have the incorrect tach drive ... the 650 and the 500 drives look almost identical, but the 650 one is a little longer and the drive gear won't reach the camshaft. It is also likely that the gauge itself is broken ... as I said ... they wear out.
Welcome aboard ...