Are you with me so far? A non-inverting stage must have a gain greater than or equal to one so you will need to use an inverting stage. OOOPS you only have a single supply so there will be a problem.
RESET. Use a gain of 1 voltage follower and drive a voltage divider with a gain of 1/6 = 0.16666.... You must use an amplifier that can withstand 30V on the input. Start your search with an LM324. There may be other requirements, that you have not articulated, that will dictate an alternate choice.
The voltage follower will prevent the divider from loading the source and you should be able to conver the 0-5V output.