Convert the polar coordinate $\left(3, \frac{5 \pi}{3}\right)$ to Cartesian coordinates. Enter exact values.
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Final Answer: $x= \boxed{\frac{3}{2}}$ and $y= \boxed{-\frac{3\sqrt{3}}{2}}$

Steps

Step 1 ：Use the formulas $x = r \cos(\theta)$ and $y = r \sin(\theta)$ to convert polar coordinates to Cartesian coordinates

Step 2 ：Given polar coordinate is $(3, \frac{5 \pi}{3})$, where $r = 3$ and $\theta = \frac{5 \pi}{3}$

Step 3 ：Calculate $x$ using the formula $x = r \cos(\theta)$: $x = 3 \cos(\frac{5 \pi}{3})$

Step 4 ：Calculate $y$ using the formula $y = r \sin(\theta)$: $y = 3 \sin(\frac{5 \pi}{3})$

Step 5 ：Simplify the values of $x$ and $y$

Step 6 ：Final Answer: $x= \boxed{\frac{3}{2}}$ and $y= \boxed{-\frac{3\sqrt{3}}{2}}$