To solve the system of equations with the provided values, we start with the equation:
\[ -5x + 6y = 17 \]
And we know that:
\[ x = -7 \]
Now, we'll substitute \(x\) with \(-7\) in the equation:
\[ -5(-7) + 6y = 17 \]
Calculating the left side:
\[ 35 + 6y = 17 \]
Next, we'll solve for \(6y\) by isolating it:
\[ 6y = 17 - 35 \]
This simplifies to:
\[ 6y = -18 \]
Now, we can solve for \(y\):
\[ y = \frac{-18}{6} = -3 \]
Thus, the solution to the equations is:
\[ x = -7, \quad y = -3 \]
The ordered pair is \((-7, -3)\).