To rotate a point \((x, y)\) counterclockwise about the origin by an angle \(\theta\), we can use the rotation transformation formulas:
\[ x' = x \cos(\theta) - y \sin(\theta) \]
\[ y' = x \sin(\theta) + y \cos(\theta) \]
In this case, our point is \((-4, 5)\) and we want to rotate it by \(270^\circ\). First, we need to determine the values of \(\cos(270^\circ)\) and \(\sin(270^\circ)\):
- \(\cos(270^\circ) = 0\)
- \(\sin(270^\circ) = -1\)
Now substituting these values into the formulas:
\[ x' = -4 \cdot 0 - 5 \cdot (-1) = 0 + 5 = 5 \]
\[ y' = -4 \cdot (-1) + 5 \cdot 0 = 4 + 0 = 4 \]
Thus, the new point after rotating \((-4, 5)\) counterclockwise about the origin \(270^\circ\) is:
\[ \boxed{(5, 4)} \]