Convert the polar coordinate $\left(2, \frac{5 \pi}{4}\right)$ to Cartesian coordinates.
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\begin{array}{l}
x= \\
y=
\end{array}
\]
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Step 1 ：Convert the polar coordinate \(\left(2, \frac{5 \pi}{4}\right)\) to Cartesian coordinates using the formulas \(x = r \cos(\theta)\) and \(y = r \sin(\theta)\) where \(r\) is the radius and \(\theta\) is the angle in radians.

Step 2 ：Given \(r = 2\) and \(\theta = \frac{5 \pi}{4}\), calculate \(x\) and \(y\).

Step 3 ：\(x = 2 \cos\left(\frac{5 \pi}{4}\right) = 2 \cos\left(3.9269908169872414\right) = -1.4142135623730954\)

Step 4 ：\(y = 2 \sin\left(\frac{5 \pi}{4}\right) = 2 \sin\left(3.9269908169872414\right) = -1.414213562373095\)

Step 5 ：Simplify the values of \(x\) and \(y\) to get the final answer.

Step 6 ：\(x= \boxed{-\sqrt{2}}\)

Step 7 ：\(y= \boxed{-\sqrt{2}}\)