1. The problem is to analyze the function $y=\sqrt{5-|x|}$.\n\n2. This function involves a square root and an absolute value. The domain is restricted by the square root, which requires the expression inside to be non-negative: $$5 - |x| \geq 0.$$\n\n3. Solve the inequality for the domain: $$|x| \leq 5.$$ This means $$-5 \leq x \leq 5.$$\n\n4. The function can be rewritten as $$y = \sqrt{5 - |x|}.$$ Since $|x|$ is always non-negative, the function decreases as $|x|$ increases from 0 to 5.\n\n5. At $x=0$, $y=\sqrt{5-0}=\sqrt{5}$. At $x=\pm 5$, $y=\sqrt{5-5}=0$.\n\n6. The graph is symmetric about the y-axis because of the absolute value. The function has a maximum at $x=0$ and intercepts at $x=\pm 5$.\n\nFinal answer: The domain is $$[-5,5]$$ and the range is $$[0,\sqrt{5}].$$