Don't look at the number of squares by height and width; that's just there to fool you.  The trick is based on your mind's assumption that the diagonal for the combined shape across that height and width is a straight line; in this case, it isn't.

If you need proof, the long side of the smaller 5x2 triangle is 2 1/2 times the length of its short side, while for the larger 8x3 triangle, it's 2 2/3 times.  So the hypotenuses are at slightly different angles, just enough so that when combined into one larger "triangle", the displaced area takes up the size of one block.