To find the value of \( k \) that satisfies the equation \(-x^2 + 5x = -x + 5\), we can first set the two equations equal to each other.
Starting with the given equation: \[ -x^2 + 5x = -x + 5 \]
Rearranging this equation gives us: \[ -x^2 + 5x + x - 5 = 0 \] \[ -x^2 + 6x - 5 = 0 \]
Multiplying through by -1 to simplify: \[ x^2 - 6x + 5 = 0 \]
Next, we can factor the quadratic: \[ (x - 1)(x - 5) = 0 \]
Setting each factor to zero gives us: \[ x - 1 = 0 \quad \text{or} \quad x - 5 = 0 \]
Thus, we find: \[ x = 1 \quad \text{or} \quad x = 5 \]
Now we compare these solutions with the values of \( k \) in the second table. The values of \( k \) given in the responses are \( 1, 4, 0, -6 \).
The value of \( k \) that is also a solution to the equation \(-x^2 + 5x = -x + 5\) is: \[ \boxed{1} \]