To find the domain of the expression \(\sqrt{5x - 2}\), we need to determine when the expression inside the square root is non-negative, since the square root of a negative number is not defined in the real number system.
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Set the expression inside the square root greater than or equal to zero: \[ 5x - 2 \geq 0 \]
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Solving for \(x\): \[ 5x \geq 2 \] \[ x \geq \frac{2}{5} \]
Thus, the domain of the expression \(\sqrt{5x - 2}\) is: \[ \boxed{[\frac{2}{5}, \infty)} \]
This means \(x\) can take any value from \(\frac{2}{5}\) to positive infinity.
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