you can get the vertex of an absolute value expression by y = | x - h | + k, where the vertex is at (h, k).
now, as a matter of transformations, the negative in front of the absolute value expresssion, means the graph of it upside-down.
the graph of | x - h | + k, is like the letter V, comes down, it makes an apex and goes right back up, the apex is of course at the vertex (h,k).
so -|x - 4| + 5, has a vertex at (4,5), and is upside-down, like Ʌ, which means, it comes from the botttom, goes up up up, hits (4,5) and then goes right back down.
so its range is from y = 5, and back down, namely to -∞, so (-∞ , 5].
