Real life producer surplus I'd like to ask a question about  producer surplus. Basically I got the concept and how we calculate when a demand or price changes on a graph, but I cannot figure out how I should apply to real life.

I mean, let's say A = 10, B = 20 and Q = 5.

At first the producers accept to sell at the price $10. Is that right? 

And the revenue they get would be  $10 \cdot 5 = 50 $   but the producers managed to sell at the price of 20 and the revenue they get is  $ 20 \cdot 5 = 100$.  

And the difference between what the producers get and what the producers would ask for is $100 - 50 = 50$.

But when I calculate producer surplus using graphic (ABC), I get  $\frac{(20 -10 ) \cdot 5} { 2 } = 25 $  

So I come to different conclusion in real life than when I calculate using graph. Why? Could anyone explain to me please?
I think you misunderstood what the supply line represents. The function takes as its argument the number of units sold. It then returns the lowest price which the supplier of the last unit requires such that he is willing to sell.

Thus, the profit would not be $10*5$. Instead, the last person willing to sell the good receives 0 profit as he is selling at the lowest price he is willing to accept. Counting in discrete units, we would have something like $10+7.5+5+2.5+0=25$ profit. Each additional seller of a unit makes less profit than the previous one.

The flaw in your logic was that the first seller can really only provide a single unit at price 10 and not 5 units. The next unit already costs a bit more in production all the way till the last unit makes its producer just break even.