visually, from that picture, it looks worn a bit.
I replaced my chain and cassette on my mountain bike about a month ago, cassette was 8 years old, chain was about 6. She now shifts like a BRAND NEW bike. It shift good before, but the chain was about 1/4" longer than the new, and the cassette was a little worn. Maybe not enough to replace, but I got 8 years out of it.
But, by the looks of it cassette and chain could be replaced. Maybe your chainrings as well? A good way to tell if cassette or chainrings need replacement is to put a new chain on them, if there is a lot of slop between teeth, time for new parts.
and always replace the chain when putting new cassettes/chainrings on. Start with all parts fresh, that way they wear in WITH eachother, and not TO eachother...
Keep your drivetrain clean, as well. I clean my chain once or twice a year, more if it needs it. When I do that, or when I install new chain, I will clean the idler cogs as well, and re-lube them. Get as much grit out of the teeth as you can...makes for a better shifting experience.