Let's solve the given equation step by step:

The equation is:

$\sqrt{a - 5} = 5$

Step 1: Eliminate the square root

To eliminate the square root, square both sides of the equation:

$(\sqrt{a - 5})^2 = 5^2$

$a - 5 = 25$

Step 2: Solve for $a$

Add 5 to both sides:

$a = 25 + 5$

$a = 30$

Final Answer:

$\boxed{30}$

Let me know if you have questions about any step!

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Relative Questions:

1. How would the solution change if the equation were $\sqrt{a - 5} = -5$?
2. What is the domain of the function $f(a) = \sqrt{a - 5}$?
3. What happens when squaring both sides of an equation? Why must you check for extraneous solutions?
4. How would you solve if the equation were $\sqrt{a - 5} + 2 = 5$?
5. Can you graph the function $f(a) = \sqrt{a - 5}$ and identify where it equals 5?

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Tip:

Always double-check your solutions when squaring both sides of an equation, as squaring can introduce extraneous solutions that may not satisfy the original equation.