[MNRICK]

Many of the teeth on your cassette look noticeably and irregularly worn, especially on the 5th and 6th cogs that you mention. If you can see this upon a quick visual assessment, it's likely your cassette should have been replaced a while ago.

The easiest way to prolong the overall life of your drive train is to make sure your chain is kept clean and lubricated, and replace it when it reaches ~.5% wear. This will be more economical in the long run as it saves wear and tear on more expensive components.

Common myth. If you replace a chain when it lengthens .5 inches, you will probably do so every 3000 or less miles. You will have to replace the cassette and chain rings in due time. I have run chains for 25000 miles and then replace all the drive bits and can do so for less than the cost of replacing the chain 8 times. And no, I have not had any issues with failure of the parts.