To solve the equation \( \sqrt{2z - 2} = 5 \), we first square both sides to eliminate the square root:
\[ 2z - 2 = 25 \]
Next, add 2 to both sides:
\[ 2z = 27 \]
Then, divide both sides by 2:
\[ z = \frac{27}{2} = 13.5 \]
Now, we can check if \( z = 13.5 \) makes the original equation true:
\[ \sqrt{2(13.5) - 2} = \sqrt{27 - 2} = \sqrt{25} = 5 \]
This confirms that the equation holds true.
Therefore, the value of \( z \) that makes the equation true is 13.5.