To rotate a point \( (x, y) \) by 90 degrees clockwise around the origin, you can use the transformation:
\[ (x, y) \rightarrow (y, -x) \]
Let's apply this transformation to each endpoint of the line segment.
For the point \( (2, -1) \):
\[ (2, -1) \rightarrow (-1, -2) \]
For the point \( (5, -4) \):
\[ (5, -4) \rightarrow (-4, -5) \]
Therefore, after rotating the segment 90 degrees clockwise, the new endpoints are:
\[ (-1, -2) \quad \text{and} \quad (-4, -5) \]