As we are told that there are 5 black squares that limits the possible arrangements. Since each of the four edges of the grid must contain an even number of black squares, they must appear in an odd number of corners. That leaves just seven distinct arrangements of black squares: four with one black corner and three with three black corners. One of the seven arrangements of black squares leads to a symmetrical solution. Five more arrangements don’t lead to any solutions.

Here is the asymmetrical solution:

And if you’re interested, here are the other 18 solutions I found: