I have had the bike for about 4/5 years with the original chain and sprockets on. So I would say about 7,000 miles???????
you need a new chain and a new cassette - simple
if you replace the chain every 1500 miles the cassette will last perhaps 8000 or more miles depending on its quality, however, using an old chain will wear the cassette much faster. In your case both items are ready for the bin! You've done very well to get 7000 before the chain has started to jump.
As for the wear, this is very hard to notice on the cassette just by looking at it. Chain wear can be checked using a tool that costs about £10; Park Tools make a good one.