Real life producer surplus
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.