Since we are "non visa" eligible I would need to apply just when I get back to UK and I never heard about it before.
Is there anyone that did that before?
You are a Brazilian national who has spent 5 months in the UK. You want to take a 4 week cooling-off period and then return and apply for a 6 month short-term student visa. Brazilians do not need an entry clearance. You claim to be familiar with the visitor rules.
So do you guys think with all those documents - flight return tickets, bank statements, letter from the school, letter from my friends about accommodation - is enough to get in again?
The answer to this question is indeterminate. What you want to do is legal, and there are no required intervals or cooling-off periods between visits. But on the other hand, the IO always has the option of refusing entry and having you removed. Moreover, the outcome of any interaction between a traveller and an Immigration Officer is wholly dependent on personal impact and articulation skills. You didn't give enough information about your personal impact to make a good guess (and we don't want all that information anyway). If you want you can hire an experienced practitioner (like a retired IO) to give you mock interviews.
BUT... BUT... The 'golden' solution for someone in your situation is to apply for entry clearance before travelling. Even though you do not need one, having one means your landing interview is much simpler and much more like a formality. It happens this way because a British consulate will have already checked you out and concluded that you are 'cleared' for entry.
Our laws say that an entry clearance must be respected by an Immigration Officer at a port (Paragraphs 25 and 25A). People who use them (but do not HAVE to have one) do so because it eases the transit of UK immigration controls and avoids wasted airfares and the distress of removal from port. Hence it's the 'golden' solution for anyone who is worried about what will happen in their landing interview.