Champions at Rank 5 and 6 are limited to Level 30 if they are not enlightened.
If you have enlightened Champions of Rank 5 and 6, you can increase their Level to 35.
To enlighten a Champion, visit the Shrine of Summoning, Champions tab, Enlightenment sub tab. To enlighten a Champion, you will need to sacrifice another one of the same Grade and Type. The sacrificed Champion will disappear.
Enlightenment Level is represented by a number on the top right of your Champion's portrait. There are 5 stages of Enlightenment, and each one boosts all the stats of your Champion.