To find the ordered pair of the endpoint in the standard form of the square root function \( y = \sqrt{5x - 4} - 1 \), we need to identify where the expression inside the square root is equal to zero:
\[ 5x - 4 = 0 \]
Solving for \( x \):
\[ 5x = 4 \ x = \frac{4}{5} \]
Now, we can substitute \( x = \frac{4}{5} \) back into the equation to find the corresponding \( y \)-value:
\[ y = \sqrt{5\left(\frac{4}{5}\right) - 4} - 1 \ y = \sqrt{4 - 4} - 1 \ y = \sqrt{0} - 1 \ y = 0 - 1 \ y = -1 \]
Thus, the endpoint of the square root function is \(\left(\frac{4}{5}, -1\right)\).
Now, let's compare this to the given options:
- \((-4, 1)\)
- \((4, 1)\)
- \((4, -1)\)
- \((-4, -1)\)
None of the options directly match \(\left(\frac{4}{5}, -1\right)\). However, it seems there may be a misunderstanding regarding how the options are construed.
If we focus only on \(y = -1\), we should take that part from our calculation. Thus, the point we calculated, \((\frac{4}{5}, -1)\), indicates that it would be related to the \(y\)-coordinate of -1.
Since the correct answer doesn't appear in your list, based on the given options, the closest relation regarding \((-1)\) is:
- The choice \((4, -1)\) since it corresponds to \(y = -1\) as well.
Therefore, based on the context given by the choices, the answer is: \[ \boxed{(4, -1)} \]
But please remember that the actual calculated endpoint was \(\left(\frac{4}{5}, -1\right)\).