To translate the line segment with endpoints \((0, 0)\) and \((5, 4)\) up 3 units and left 2 units, we need to adjust the coordinates of each endpoint accordingly.
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For the endpoint \((0, 0)\):
- Up 3 units: \(0 + 3 = 3\)
- Left 2 units: \(0 - 2 = -2\)
- New coordinates: \((-2, 3)\)
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For the endpoint \((5, 4)\):
- Up 3 units: \(4 + 3 = 7\)
- Left 2 units: \(5 - 2 = 3\)
- New coordinates: \((3, 7)\)
Thus, after the translation, the new endpoints of the line segment are \((-2, 3)\) and \((3, 7)\).