For the point given in polar coordinates, state the quadrant in which the point lies if it is graphed in a rectangular coordinate system. \[ \left(5,135^{\circ}\right) \] The coordinate $\left(5,135^{\circ}\right)$ lies in quadrant II III. I. IV.

Step 1 ：Given the polar coordinates \((5,135^{\circ})\).

Step 2 ：Convert the angle from degrees to radians. In Python, this can be done using the math.radians function. The angle in radians is approximately \(2.356194490192345\).

Step 3 ：Convert the polar coordinates to rectangular coordinates. In Python, this can be done using the math.cos and math.sin functions for the x and y coordinates respectively. The rectangular coordinates are approximately \((-3.54, 3.54)\).

Step 4 ：Since both x and y are positive, the point lies in the second quadrant of the rectangular coordinate system.

Step 5 ：Final Answer: \(\boxed{II}\).