... have to change my chain soon - Its only done about 5300km but I didn't look after it for the first half of that :/
Would that have been before or after I mentioned it to you in this thread?

5,300 km is a very poor life for a chain on a small bike. Even on my 1200 Bandit I'd normally expect to get 20,000 to 30,000km (but a few years ago I swapped it for an FJR -- mainly because the FJR is shaft drive, so chains aren't an issue for my touring bike any more

Having said that, I suspect that in addition to poor maintenance you might have had a cheap chain to begin with. Do you know who its manufacturer was? Chinese?
if I pull the back link away from the sprocket when the chain is adjusted properly it barely moves but there isn't much adjustment left so I take it that means it needs to go?
Chains rarely wear evenly, especially if neglected. Check it at several positions. Rotate the rear wheel a turn or so between each check.
I'm assuming since it isn't a big bike that the chain has a split link. If not you'll need a chain riveting tool to do anything with the chain, or you'll have to take out the swinging arm to change the chain.
Don't rely on the amount of movement left on the chain adjuster to decide if the chain is OK. If it sits well on the sprockets with no risk of riding up and coming off them then it should be OK to take half a link or a link out. Half a link sounds silly but it's possible.

I have a new chain for it and I know how to change it but it will be the biggest bit of maintenance I've done so far
I hope you bought a decent chain.
It's usually advisable to replace the sprockets and the chain together. Worn sprockets can wear a new chain very quickly. It's less of an issue on a smaller machine but it's still an issue. Look carefully at the sprockets, most importantly at the one on the gearbox end of the chain (because it's a lot smaller than the one on the wheel and tends to wear faster). If the teeth show any sign of being hook-shaped instead of symmetrical then you should replace the sprockets or you're just wasting money on the chain.
Sprockets aren't all that expensive but replacing them is a bigger job than replacing the chain. Don't attempt it if you aren't confident. A chain flying off the sprockets at speed can cause a very nasty accident.