1. **State the problem:** Determine if the piecewise function $$f(x) = \begin{cases} 2x - 1, & x < 5 \\ x^2, & x \geq 5 \end{cases}$$ is continuous on the interval $(5, 8]$. 2. **Recall the definition of continuity on an interval:** A function is continuous on an interval if it is continuous at every point in that interval. Since $(5,8]$ excludes 5 but includes 8, we only need to check continuity for $x$ in $(5,8]$. 3. **Analyze the function on $(5,8]$:** For $x \geq 5$, the function is defined as $f(x) = x^2$, which is a polynomial function. 4. **Properties of polynomial functions:** Polynomial functions are continuous everywhere on the real line. 5. **Conclusion:** Since on $(5,8]$ the function equals $x^2$, which is continuous, $f(x)$ is continuous on $(5,8]$. 6. **Note:** The question does not ask about continuity at $x=5$, so the behavior at $x=5$ is not relevant here. **Final answer:** $f(x)$ is continuous on the interval $(5,8]$.