To rotate a point \( (x, y) \) by \( 180^\circ \) clockwise, the formula used is to simply negate both coordinates.
Starting with the point \( (3, -5) \):
- The new coordinates after a \( 180^\circ \) rotation are:
\[ (-x, -y) = (-3, 5) \]
Thus, the new point after rotating \( (3, -5) \) \( 180^\circ \) clockwise is \( (-3, 5) \).