The 30 minute break in your Pomodoros is to be used to go into what is called "diffuse" mode, where your mind can roam freely. The point of the breaks are to allow your mind to cement what you have learned (like building a muscle) and help propel you forward by giving you rewards to look forward to.
Obviously what you'll probably want to do in this break is to eat something, considering that the short 5 minute breaks don't allow enough time for that (especially if you're doing back-to-back Pomodoro sets). Other things to do can include activities such as walking in the park, looking at the clouds, meditating, riding in a car, or some physical activity. Exercise, such as jogging, is extremely helpful (It's better than any drug in regards to learning). I've also heard many people say that they get their best ideas when exercising (hiking, etc).
Of course, don't do things that involve a lot of focus and concentration (since you are reserving that for the actual Pomodoros). I've heard some answers saying to do something involving electronics, but I have heard several people say that it is generally not good to check electronics during your breaks. For me personally (as a knowledge worker), I have to completely break away from my electronics during my breaks as a change of pace or it will reduce my concentration.
Meditation and naps are great ideas. Nothing wrong with taking a walk either! – Zaz – 2016-10-18T22:37:50.163
shouldn't you have a break instead of writing this question? – Ooker – 2016-12-22T10:22:49.163