1. The problem consists of finding the distance between two points in the coordinate plane: $(-x,1)$ and $(-5,7)$. 2. Use the distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$, which is $$d=\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$. 3. Substitute the given points into the formula: $$d=\sqrt{(-5 - (-x))^2 + (7 - 1)^2}$$. 4. Simplify inside the radical: $$d=\sqrt{(-5 + x)^2 + 6^2}$$. 5. Further simplification gives: $$d=\sqrt{(x - 5)^2 + 36}$$. 6. This expression represents the distance between the points in terms of $x$. 7. If you want a numerical value, you need to know $x$; otherwise, this is the simplified distance formula.