"Since the chain was 5 years old and very weared out and since the rear cassette was also wared out, I have bought and mounted the following new cassette and chain" sounds a lot like the chainrings are worn out too. Replacing them or at least the most used one or two should help.
Edit: The picture confirms it. The teeth on chainrings have worn into sharp and slightly asymmetric "shark fins" that are the hallmark of worn out chainring.